Cook the sausage in a large skillet over medium-high heat until it is browned and crumbly, allowing it to develop flavor as it cooks.
Check the amount of fat left in the pan and add butter if needed so there are about three tablespoons of fat in total.
Sprinkle the flour over the cooked sausage, stirring well so it absorbs the fat and begins to cook, turning slightly golden.
Pour in the milk gradually while stirring continuously to create a smooth mixture without lumps.
Let the gravy simmer over medium heat, stirring occasionally, until it thickens to your desired consistency.