In a medium saucepan over medium heat, melt the butter. Add the flour and cook, stirring constantly, for about 2 minutes. Do not let the mixture brown.
Gradually pour in the milk in a steady stream, whisking constantly. Bring the mixture to a boil. Reduce the heat to medium-low and let simmer until the sauce is smooth and thickened, about 8 to 10 minutes. Season to taste with salt and pepper.
Makes about 2 cups.