Preheat your oven to 375°F (190°C). Grease the baking dish with butter or spray with cooking spray to prevent sticking.
In a large mixing bowl, whisk together the eggs, milk, salt, and black pepper until the mixture is smooth and slightly frothy.
Stir in the shredded cheese, diced vegetables, and cooked meats (if using), ensuring an even distribution throughout the egg mixture.
Pour the mixture into the prepared baking dish, spreading evenly with a spatula for uniform thickness.
Bake in the preheated oven for approximately 35 minutes, or until the top is golden brown and the casserole is set around the edges. You should hear a gentle bubbling, and the edges may lightly pull away from the dish.
Remove from the oven and allow to cool for 5 minutes. Slice into squares and serve warm, revealing a fluffy interior with a crisp top layer.