Preheat the oven to 350°F. Lightly coat a 9×13-inch baking dish with nonstick cooking spray.
Cook the breakfast sausage in a large skillet over medium heat, breaking it into crumbles. Continue cooking until browned and fully cooked.
Sprinkle the flour over the cooked sausage and stir until the sausage is evenly coated. Cook for one minute.
Slowly pour 2½ cups of milk into the skillet while stirring. Add the black pepper and salt. Continue cooking until the gravy thickens, about five to seven minutes. Remove it from the heat.
Cut each refrigerated biscuit into four pieces and spread the pieces evenly across the bottom of the prepared baking dish.
Sprinkle about half of the cooked sausage gravy over the biscuit pieces.
Whisk the eggs with ½ cup of milk in a separate bowl. Pour the egg mixture evenly into the baking dish.
Sprinkle the shredded cheddar cheese over the eggs. Spoon the remaining sausage gravy evenly over the top.
Bake uncovered for 35–45 minutes, or until the biscuits are golden, the eggs are set, and the center reaches 160°F.
Allow the casserole to rest for five to ten minutes before slicing and serving.