Preheat the oven to 350F
Heat the olive in a pan over medium heat. Add the chopped broccoli, onions, and garlic. Add a little salt and pepper and cook for several minutes, tossing a few times until broccoli is tender.
If making your own pie crust, bake it for 8 minutes. If using a store-bought pie crust (make sure it's thawed fully if frozen), warm it for 3 minutes in the oven.
Egg filling: add the eggs, milk, and parmesan cheese to a mixing bowl and whisk well. Season with the remaining salt and pepper.
Layer ¾ cup of the shredded cheddar and mozzarella cheese into the bottom of the warm pie crust.
Pour the egg mixture over the cheese. Sprinkle the remaining ¼ cup of cheese.
Bake at 350F for 45-60 minutes. Cool for 5-10 minutes.