Set a rack in the top third of the oven and preheat to 300°F. Grease a 12-cup standard muffin tin.
In a large bowl, thoroughly whisk eggs, water, salt, and pepper. Fold in tomatoes, green onions and spinach. Swirl in pesto.
Evenly distribute the mixture into the wells of the muffin tin, using about 1/3 cup each. Top with about 1 Tbl mozzarella per well. Bake until the egg bites puff up and the tops no longer look wet, 25 to 30 minutes. (The egg bites will puff dramatically in the oven but collapse once cooled.)
Let cool slightly, then remove the egg bites from the tin using an offset spatula or butter knife.