Cook the breakfast sausage in a skillet over medium heat, breaking it into small pieces, until fully browned. Drain the excess grease and set aside.
In a large bowl, whisk together the eggs, milk, salt, and black pepper until smooth and well combined.
Grease a baking dish and spread the cooked sausage evenly across the bottom. Add the bread cubes or potatoes if using, then sprinkle the cheese evenly over the top.
Pour the egg mixture evenly over all the ingredients, making sure it settles throughout the dish.
Bake in a preheated oven until the eggs are fully set and the top is lightly golden.
Allow the casserole to rest for a few minutes, then slice and serve warm.