Brown the breakfast sausage over medium heat in a large skillet, breaking it into crumbles as it cooks. Once fully cooked, drain any excess grease and set aside. I sometimes let the sausage cool for a few minutes so it doesn't melt the cheese when assembling.
Grease a 9×13 inch casserole dish or large baking dish with cooking spray or butter. Cube the slices of white bread and spread them evenly in the bottom of the greased dish.
Evenly distribute the cooked and crumbled sausage (from Step 1) over the cubed bread in the pan. Sprinkle the shredded cheddar cheese over the top, making sure it's distributed evenly.
In a large bowl, whisk together the eggs until smooth. Add the whole milk, salt, and freshly ground black pepper. Continue whisking until the mixture is well combined. Pour this egg mixture evenly over the layered bread, sausage, and cheese in the baking dish.
Cover the dish tightly with plastic wrap or aluminum foil. Refrigerate overnight so the bread can absorb the egg mixture thoroughly, resulting in a custardy and cohesive casserole.
Preheat the oven to 325°F (163°C). Remove the casserole from the refrigerator and let it sit at room temperature for about 20 minutes. Uncover the dish and bake for about 45 minutes, or until the center is set and a knife inserted comes out clean. I like to let it cool slightly after baking so it slices more easily.
Cut the baked casserole into squares directly in the pan and serve warm. For extra flavor, you can garnish with freshly cracked black pepper or some chopped herbs before serving.