The idea of eggs comes up frequently in the book. With each mention we're reminded that they're part of a human woman's reproductive cycle, even though usually what the narrator is doing is eating them. She usually has them for breakfast, eating eggs so she can make her own healthy eggs. When, one night, she falls asleep in her closet and terrifies Cora into dropping her breakfast the next morning, it's an egg that falls to the ground and has to be thrown away.
One day at breakfast the narrator thinks, "I think that this is what God must look like: an egg [...] To look at the egg gives me intense pleasure" (19.11, 12). She adds that she is living "The minimalist life. Pleasure is an egg. Blessings that can be counted, on the fingers of one hand. But possibly this is how I am expected to react. If I have an egg, what more can I want?" (19.15). The narrator's attitude toward eggs alludes to what eggs symbolize in Christianity:
The egg is a wonderful symbol of birth and rebirth, an apparently lifeless object out of which comes life. [...] It is a symbol of Christ's Resurrection. [...] The egg represents the Creation, the elements, and the world itself, with the shell representing the firmament, the vault of the sky where the fiery stars lie; the thin membrane symbolizing air; the white symbolizing the waters; and the yolk representing earth. (source)
If the egg can be seen to contain God and pleasure, a whole world, the narrator wonders, perhaps she should not desire anything else. In her next thought, however, she worries that she's been given the egg and these feelings so she won't want anything else. Even philosophical abstraction and meditation has been undermined by Gilead.