In a large skillet, cook the sausage over medium heat until cooked through and nicely browned, about 15 to 20 minutes. Transfer the sausage to a platter and set aside.
Add butter into the rendered grease in the skillet, scraping the pan to incorporate any browned bits. Once the butter is melted, whisk in the flour until smooth. Then, whisk in the milk 1 cup at a time, making sure to get any lumps out until the mixture is smooth. Bring to a simmer over medium heat and cook until slightly thickened, about 5 minutes.
Stir the sausage into the gravy. Season generously with salt and pepper. Serve warm.
Store leftovers in a covered container in the refrigerator for up to 4 days. Reheat gently over low heat.