In a large skillet over medium heat, cook and crumble sausage until no longer pink, about 8 minutes.
Stir in the butter until melted, then sprinkle with flour. Stir and cook for 1 minute until flour is absorbed.
Add the milk gradually, stirring constantly so there are no lumps.
Bring to a simmer, stirring occasionally. This may take 8-10 minutes. After coming to a simmer with lots of bubbling, let cook for 2 full minutes or until thickened. Gravy will continue to thicken as it cools.
Stir in salt and pepper. Taste and adjust seasoning if necessary.