Shred zucchini and pat with paper towel to remove moisture. Heat olive oil in a small skillet over medium-low heat. Add zucchini and cook for 2 minutes. Lightly season with salt and pepper.
Make a "well" for the egg. Not so much that the egg will be on the bare pan, but enough to give it a place to nestle in and stay put. Crack the egg and add to the well. Move the white around a bit to distribute it throughout the zucchini.