Preheat your oven to 350°F (175°C). Generously coat a 9-by-13-inch baking dish with nonstick spray to prevent sticking.

In a sizable skillet set over medium heat, crumble and brown the sausage until thoroughly cooked, leaving the rendered fat in the pan for flavor.

Dust the browned sausage with the flour and stir to coat evenly. Gradually incorporate the 2 1/2 cups of milk, stirring constantly to avoid lumps. Allow the mixture to simmer gently until thickened, approximately 5 to 7 minutes. Season the gravy lightly with salt and black pepper, then take off the heat.

Cut each biscuit into four pieces and distribute them evenly across the base of the prepared baking dish.

Pour the sausage gravy over the biscuit quarters, making sure to cover them thoroughly.

In a separate mixing bowl, whisk together the eggs, the remaining 1/2 cup of milk, and a dash of salt and pepper. If using cheddar, fold it into the egg mixture. Carefully pour the egg mixture over the sausage gravy layer in the dish.

Place the dish in the preheated oven and bake uncovered for 35 to 40 minutes, or until the top turns golden and the center is firm to the touch, indicating that the eggs have set and the biscuits are cooked through.

Allow the casserole to sit for 5 to 10 minutes post-baking. Slice and serve warm.