In a large skillet or saucepan, cook the breakfast pork sausage over medium heat, breaking it up into crumbles, until browned and cooked through. Remove the cooked sausage from the skillet, leaving the drippings.
In the same skillet, melt the butter over medium heat. Add the all-purpose flour and whisk continuously until it turns golden brown, creating a roux.
Gradually pour in the milk while whisking constantly to prevent lumps from forming. Continue cooking and stirring until the gravy thickens and reaches your desired consistency.
Return the cooked sausage to the skillet with the gravy. Stir well to combine. Season with salt and pepper to taste.
If desired, you can thicken the gravy further by adding a cornstarch slurry. In a small bowl, mix together 1 tablespoon of cornstarch and 2 tablespoons of water to create the slurry. Slowly pour the slurry into the gravy while stirring continuously. Cook for an additional minute to allow the gravy to thicken.