While the crust is baking, make the filling. In a large bowl, whisk together the eggs, milk, half and half, salt, and pepper until there are no streaks of eggs left. Stir in the cheese, cooked ham, and green onions.
5 large eggs, 3/4 cup milk, 1/2 cup half and half, 1/2 teaspoon kosher salt, 1/4 teaspoon black pepper, 1 cup cheese, 1 cup cooked ham, 4 green onions