Heat oven to 400 F.
Heat 1 teaspoon of oil in a large skillet or frying pan that can be placed inside your oven. An iron skillet is a great option.
Add the onions and saute until clear and soft. Add the mushrooms and squash and cook for 2-3 minutes until tender. If there's too much fluid in the pan, drain most of it.
Meanwhile, beat the eggs in a medium size bowl. Mix in the cilantro and ¾ cup mozzarella cheese. Season with a little bit of salt and pepper.
If your vegetables are sticking to the pan, add another 1 teaspoon oil. Pour the egg mixture over the vegetables. Stir to make sure everything is equally spread. Cover the pan with a lid, lower the temperature, and cook for 8 minutes or until the eggs are almost set.
Place in the oven and cook for 5 minutes until the eggs are completely set.
Top with the remaining cheese.