Cook both of the sausage meats in large nonstick skillet over medium-high heat, breaking the meat up with the spoon, until browned and cooked through. Using a slotted spoon, transfer the meat to a bowl.
Remove all but 3 tablespoons of the fat from the skillet.
Sprinkle the flour into the skillet, stir well, and cook over medium-high heat for 1 minute, stirring constantly. Remove from the heat.
Slowly add the milk and the broth, whisking constantly until the mixture is smooth. Return the skillet to the heat and cook until the gravy is slightly thickened, 2 to 3 minutes.