In the Cleft of the Rock

Avivah Zornberg (The Particulars of Rapture p. 436)
This is the point where the narrative digresses, apparently, from the agenda of national forgiveness and renewal to the private, mystical concerns of Moses. God's face, and His back, become literalized in a way that even the Revelation at Mount Sinai has not approached: God's hand will cover Moses' face and will uncover it; he will see one part of God but not the other.

Rabbi Chanan Morrison (adapted from Sapphire From the Land of Israel) Based on the above midrash
There are two levels of knowledge. The first is an accurate knowledge of an object’s true nature. The second is a limited knowledge, restricted by our intellectual or physical limitations. Regarding tangible objects, there may not be a significant difference between the two levels of knowledge. But when dealing with abstract concepts, especially with regard to the nature of God, the difference will be great — perhaps infinitely so.
The imagery of God’s ‘face’ and ‘back’ corresponds to these two levels of knowledge. ‘Face’ in Hebrew is panim, similar to the word p'nim, meaning inner essence. True knowledge of God’s infinite reality is God’s ‘face.’
Knowledge of God’s reality according to our limited understanding, on the other hand, is referred to as God’s ‘back.’ Moses was granted this partial, indirect knowledge — a grasp of the Divine that we are able to appreciate and apply in our finite world.
(Teaching of Rav Kook)

Rabbi Rachel Barenblatt (The Velveteen Rabbi)
Jewish tradition interprets these verses the way we interpret all anthropomorphic descriptions of God in Torah -- as metaphor. God doesn't really have a face, nor a hand with which to shelter Moshe in the cleft of the rock, nor a back which Moshe might glimpse as God departs. These are human conceptions. We can't wrap our minds around the reality of what God is, so we mentally create God in an image we can understand.
I can relate to Moshe's request. It makes sense to me that he yearned for this kind of encounter. He wanted to encounter God panim el panim, face to face, presence to presence. He wanted a radical I/Thou connection with God -- and who could blame him? Instead, what he gets is a partial glimpse of a totality too great for him to comprehend.
Moshe can't grasp the wholeness of God from within the limited perspective of a single human mind. If he were to encounter all of what God is, his individual selfhood would disappear; the orderly limits of his mind would shatter. God gives Moshe only what he can handle. He can see God's goodness. He can listen to the recitation of one of God's names, which contains compassion and mercy along with remembrance of our misdeeds. And he can glimpse something of the divine Presence as it passes him by.
I don't think this passage is only about Moshe. I think it speaks to us, too. Where can we see God's goodness manifest? What are the names of God which we receive on the frequencies to which we are attuned? What afterimage of God's presence, as it were, are we able to perceive in the world around us?

Avivah Zornberg (p. 437)
The question of structure emerges with compelling force: how does Moses' desire for personal mystical revelation mesh with the narrative of sin and forgiveness? It is remarkable that while he speaks in the first person sin gular when he asks for the vision of God's glory, he modulates to the first person plural in v 9: "If I have gained your favor... let God go in our midst... pardon our iniquity and our sin, and take us for Your own!" At the culmination of Moses' work of prayer, he identifies with the sin of the people; quietly, undramatically, the pronouns change. The fire in his bones is, by this point, so thoroughly integrated that it sparks out unselfconsciously in his syntax... he speaks with a quiet normalcy that seems to emerge seamlessly from the vision he has just experienced.
His reference to "our sin" is set in high relief against his earlier pronouns. Reproaching the people, he used the rhetoric of "You... I" "You have sinned- I shall go up...I shall atone for your sin." Pleading with God, he spoke of "this people... their sin... Erase me... (32:30-33). It is only in the prayer that leads to the vision of the cave and to God's final forgiveness that Moses begins to modulate from I to we: "For how shall it be known that Your people have gained Your favor unless you go with us, so that we may be distinguished, Your people and I, from every people on the face of the earth?" (33:16).
God's reply still focuses on Moses' personal grace as the reason for His favor. Only after the revelation of the cave does Moses make the last movement to full solidarity with the people: "Pardon our iniquity and our sin..."