In a large skillet over medium-high heat, brown sausage. Once browned, remove the sausage from the skillet and set aside. Do not drain.
Into the same skillet with the sausage drippings, on medium heat, add 4 Tablespoons unsalted butter.
Once the butter is melted, add 1 cup flour. Stir with a wooden spoon; it will be very thick.
Once it looks like a thick paste, slowly add in the milk, stirring frequently to mix it all together. Continue to add milk until the gravy reaches the desired consistency.
Add reserved sausage and stir to combine. Season with salt and pepper to taste.
Notes
More than ½ cup of milk might be required to achieve your desired thickness.