My Psalms lecturer — Dr John Kleinig — suggests that Exodus 34:5–7 plays a key role in Hebrew theology.
Walter Brueggemann, in his book Deep Memory, Exuberant Hope, explains in detail (see below).
To help analyze such texts, I have created and shared a visual filter for Logos Bible Software:
This allows one to easily see which words/sections of an OT passage share a common vocabulary with YHWH's Ex 34 covenant promise:

Walter Brueggemann, 2000, 'Deep Memory, Exuberant Hope: Contested Truth in a Post-Christian World', Fortress Press, Minneapolis, MN. The first crisis I will comment upon is the violation of the Sinai covenant in the incident of the golden calf in Exodus 32. According to conventional source criticism, Exodus 32–34 follows in the “early source” immediately after the Sinai events of theophany and covenant in Exodus 24. That is, the materials in chapters 25–31, whether later or not, are in any case of a very different kind, from a different source. The crisis of covenant-breaking, in this narrative, concerns the sin of Aaron and Israel in the making of the calf (32:30–31), Yahweh’s resolve to punish (vv. 33–34), and the plague against Israel instituted by Yahweh (v. 35). It is clear that Israel’s life with Yahweh is in jeopardy. (It is of course exceedingly difficult to determine what is “historical” in this narrative. First, the text in some important way is linked to the later narrative account of 1 Kings 12, thus making one extremely cautious about any “historicity” in Exodus 32. Second, the “facticity” of the Sinai tradition is exceedingly problematic, no doubt shaped as it is for ideological purposes. I do not purpose to adjudicate the relationship between “historical” and ideological elements in the text, but to take the text, as it is surely intended, as a paradigmatic account of covenantal crisis.) Even though we recognize the problematic character of the text, for our purposes it is enough to see that this text witnesses to a crisis in which we may attend to Israel’s “most characteristic speech.” After the tense negotiations between Yahweh and Moses in chapter 33, wherein Moses seeks assurances from Yahweh for Israel’s continued life, we arrive at chapter 34, at the awesome theophany Yahweh has just promised in 33:21–23. This theophany is enormously important for Moses and Israel, for on it hangs the potential for Israel’s political future. Moreover, the theophany is as dangerous as it is important, for there is an unresolved fierceness about Yahweh in this confrontation.
The dangerous coming of Yahweh (34:5) eventuates in the utterance of Yahweh (34:6–7). We arrive at the first of our three texts that I take as “most characteristic” of Israel’s speech. The text is situated in and evoked by the fracture of the covenant of Sinai. Yahweh would not have spoken in this way if there had not been the violation of covenant. It is not known in this moment of the covenant whether Israel can survive its disastrous affront against Yahweh. And if the possibility of covenant is not known, then it is also not known if Israel has any future in the world. Everything for Israel, everything theological and sociopolitical, depends upon this utterance of Yahweh evoked by the crisis of broken covenant.
So now Yahweh speaks. Israel receives from Yahweh in this awesome moment a divine oracle, an utterance out of God’s own mouth (34:6–7). It is Yahweh, in the crisis, who is permitted now to speak as Yahweh has never before spoken in Israel. Or should we better say, Yahweh is now required to speak as Yahweh has never had to speak before. The crisis for Israel is deep and irreversible, and now Israel’s text gives an offer of Israel’s “most characteristic speech,” expressed as divine oracle, as an utterance on God’s own lips. The oracle is in two parts. In the first part, Yahweh presents Yahweh’s own self as utterly faithful and generous:
Many scholars have noted that this originary speech in God’s mouth stands at the beginning of a major theological trajectory, to which Israel repeatedly returns. In its hymns of praise Israel speaks about God in these terms, for example, Ps. 111:4–9 and 145:8–9. In its prayers of complaint, Israel speaks to God in these terms, urging God to act in ways consistent with this self-announcement, for example, Ps. 86:15. It is clear to Israel, here and subsequently, that this cluster of terms, given as divine oracle, provide the basis for life beyond the crisis. Israel will stake everything on its capacity and will to move beyond the disruption. Yahweh’s characteristic speech, however, is not yet finished. The oracle continues in v. 7b:
This allows one to easily see which words/sections of an OT passage share a common vocabulary with YHWH's Ex 34 covenant promise:
Walter Brueggemann, 2000, 'Deep Memory, Exuberant Hope: Contested Truth in a Post-Christian World', Fortress Press, Minneapolis, MN. The first crisis I will comment upon is the violation of the Sinai covenant in the incident of the golden calf in Exodus 32. According to conventional source criticism, Exodus 32–34 follows in the “early source” immediately after the Sinai events of theophany and covenant in Exodus 24. That is, the materials in chapters 25–31, whether later or not, are in any case of a very different kind, from a different source. The crisis of covenant-breaking, in this narrative, concerns the sin of Aaron and Israel in the making of the calf (32:30–31), Yahweh’s resolve to punish (vv. 33–34), and the plague against Israel instituted by Yahweh (v. 35). It is clear that Israel’s life with Yahweh is in jeopardy. (It is of course exceedingly difficult to determine what is “historical” in this narrative. First, the text in some important way is linked to the later narrative account of 1 Kings 12, thus making one extremely cautious about any “historicity” in Exodus 32. Second, the “facticity” of the Sinai tradition is exceedingly problematic, no doubt shaped as it is for ideological purposes. I do not purpose to adjudicate the relationship between “historical” and ideological elements in the text, but to take the text, as it is surely intended, as a paradigmatic account of covenantal crisis.) Even though we recognize the problematic character of the text, for our purposes it is enough to see that this text witnesses to a crisis in which we may attend to Israel’s “most characteristic speech.” After the tense negotiations between Yahweh and Moses in chapter 33, wherein Moses seeks assurances from Yahweh for Israel’s continued life, we arrive at chapter 34, at the awesome theophany Yahweh has just promised in 33:21–23. This theophany is enormously important for Moses and Israel, for on it hangs the potential for Israel’s political future. Moreover, the theophany is as dangerous as it is important, for there is an unresolved fierceness about Yahweh in this confrontation.
The dangerous coming of Yahweh (34:5) eventuates in the utterance of Yahweh (34:6–7). We arrive at the first of our three texts that I take as “most characteristic” of Israel’s speech. The text is situated in and evoked by the fracture of the covenant of Sinai. Yahweh would not have spoken in this way if there had not been the violation of covenant. It is not known in this moment of the covenant whether Israel can survive its disastrous affront against Yahweh. And if the possibility of covenant is not known, then it is also not known if Israel has any future in the world. Everything for Israel, everything theological and sociopolitical, depends upon this utterance of Yahweh evoked by the crisis of broken covenant.
So now Yahweh speaks. Israel receives from Yahweh in this awesome moment a divine oracle, an utterance out of God’s own mouth (34:6–7). It is Yahweh, in the crisis, who is permitted now to speak as Yahweh has never before spoken in Israel. Or should we better say, Yahweh is now required to speak as Yahweh has never had to speak before. The crisis for Israel is deep and irreversible, and now Israel’s text gives an offer of Israel’s “most characteristic speech,” expressed as divine oracle, as an utterance on God’s own lips. The oracle is in two parts. In the first part, Yahweh presents Yahweh’s own self as utterly faithful and generous:
The LORD, the LORD, a God merciful and gracious, slow to anger, and abounding in steadfast love and faithfulness, keeping steadfast love for the thousandth generation, forgiving iniquity and transgression and sin … (vv. 6–7a)What is important for us is that this oracle provides most of the working vocabulary whereby Israel will subsequently (as, for example, in the Psalms) speak to God and about God. This rich array of terms … merciful, gracious, steadfast love, faithfulness, forgiving … bespeaks a God who is generous in fidelity, thus providing a basis for Israel’s future, even after the disaster of Exodus 32. It is in this crisis that Israel hears (not speaks!) its most characteristic “God-talk,” that it had not heard before. It is, moreover, to the crisis that God’s oracle speaks, for the oracle asserts that even the episode of the golden calf has not nullified God’s covenantal fidelity for Israel.
Many scholars have noted that this originary speech in God’s mouth stands at the beginning of a major theological trajectory, to which Israel repeatedly returns. In its hymns of praise Israel speaks about God in these terms, for example, Ps. 111:4–9 and 145:8–9. In its prayers of complaint, Israel speaks to God in these terms, urging God to act in ways consistent with this self-announcement, for example, Ps. 86:15. It is clear to Israel, here and subsequently, that this cluster of terms, given as divine oracle, provide the basis for life beyond the crisis. Israel will stake everything on its capacity and will to move beyond the disruption. Yahweh’s characteristic speech, however, is not yet finished. The oracle continues in v. 7b:
… yet by no means clearing the guilty, but visiting the iniquity of the parents upon the children and the children’s children, to the third and the fourth generation.Yahweh is shown to be tough and unaccommodating. That also is given in the divine oracle. Thus the same Yahweh who in vv. 6–7a is so generously for Israel, in v. 7b is so ominously demanding and threatening against Israel. Israel is not yet through the crisis, not yet assured of a future, because the very oracle that offers assurance, in the next breath takes away any certain assurance. It is no wonder that in vv. 8–9 Moses responds by promptly bowing toward the earth in worship, acting with profound deference. Moses offers a prayer that confesses the sin of Israel and seeks pardon for Israel:
If now I have found favor in your sight, O Lord, I pray, let the Lord go with us. Although this is a stiff-necked people, pardon our iniquity and our sin, and take us for your inheritance.It is as though Moses has spotted the deep contradiction between vv. 6–7a and v. 7b, and seeks assurance that Yahweh will act out of the great terms of fidelity in vv. 6–7a. In v. 10, Yahweh responds to Moses’ passionate prayer, and agrees to be the faithful God of vv. 6–7a for Israel:
I hereby make a covenant. Before all your people I will perform marvels, such as have not been performed in all the earth or in any nation; and all the people among whom you live shall see the work of the LORD; for it is an awesome thing that I will do with you.Now, finally, after deep risk and danger, Israel is through the crisis and out of jeopardy. It is God’s speech of faithfulness and steadfast love, of mercy and graciousness, of a promise of forgiveness, speech never before uttered, that is the basis of Israel’s future with Yahweh and in the world. It is no surprise that this divine oracle emerges as a “characteristic speech” in Israel about God. The great words uttered (raḥum, ḥanun, ḥesed, ’emeth) are embedded in a sentence attributed to Yahweh, situated in a divine oracle that serves as God’s own announcement of God’s self. Speech cannot become anymore elemental and primordial than this. And so we have a datum for Israel’s “God talk,” evoked in crisis, serving to resolve the crisis of broken covenant. Note well, that while v. 7b adds vocabulary that is threatening and dangerous, the option taken by Yahweh in v. 10 seems promptly to remove the statement of v. 7b from Israel’s most characteristic speech.