Preheat the oven to 350°F (175°C) and lightly grease a 9x13 inch baking dish.
Cut each raw biscuit into quarters and layer them evenly across the bottom of the prepared baking dish.
In a large skillet over medium-high heat, cook the breakfast sausage until browned and crumbled; do not drain the rendered fat.
Sprinkle the flour over the cooked sausage and stir constantly for 1 to 2 minutes to create a roux.
Gradually pour in 2.5 cups of milk while whisking constantly. Continue to cook until the gravy thickens to a coating consistency. Season with salt and black pepper.
In a medium bowl, whisk together the 6 eggs and 1/2 cup of milk, then pour this mixture over the biscuit pieces in the baking dish.
Pour the warm sausage gravy evenly over the egg and biscuit layers.
Top the casserole with the shredded cheddar cheese.
Bake in the preheated oven for 35 to 40 minutes, or until the biscuits are cooked through and the eggs are set.
Remove from the oven and allow to rest for 5 minutes before slicing and serving.