Preheat the oven to 350°F (175°C) and lightly grease a 9x13-inch casserole dish with oil or cooking spray.
Crack the eggs into a large mixing bowl.
Add the milk, melted (and slightly cooled) butter, salt, and pepper to the eggs, then whisk until well combined and slightly frothy.
Pour the egg mixture into the prepared casserole dish, spreading it evenly.
Bake for 12 minutes, then remove from the oven and use a fork or spatula to gently pull through the eggs and break them into curds.
Return the dish to the oven and bake for an additional 8 minutes.
Remove from the oven and use a fork to stir the top so any remaining runny egg is incorporated; the residual heat will finish cooking the eggs.