Cook sausage in a large skillet over medium-high heat until browned and crumbly, 5 to 7 minutes. Transfer sausage to a plate, leaving drippings in the skillet.

Add bacon grease to the sausage drippings, and reduce the heat to medium. Whisk in flour and stir constantly until mixture becomes paste-like and turns golden brown, about 5 minutes.

Gradually whisk in milk until smooth. Bring to a simmer, then return sausage to the skillet and season with salt and pepper. Cook, stirring occasionally, until mixture is smooth and thick, 10 to 15 minutes.