In a cast-iron skillet, cook the sausage over medium-high heat until browned and the fat is rendered, 4 to 5 minutes. Reduce the heat to medium-low, add the butter, stir to melt, then gradually sprinkle in the flour and cook until the sausage is coated and the flour is absorbed, about 2 minutes.
Add the milk, return the heat to medium-high, and cook, stirring, until thick, about 10 minutes. (This requires patience, but stirring is sort of like meditation. Keep telling yourself this as you stir.)
Add the black pepper, sage, salt, and red pepper flakes and cook, stirring, 2 minutes more. Remove from the heat and cover to keep warm.