Melt the butter in a small saucepan over medium heat. Add the flour and cook, stirring constantly with a wooden spoon, to make a light roux, 1 minute to 90 seconds. (Do not allow the roux to brown.) Gradually add the milk, whisking constantly until the sauce thickens and comes to a boil, 2 to 3 minutes. Reduce the heat to a simmer, add the salt and pepper, stir well and let simmer 1 minute. Add the cheese and whisk until melted. (If the sauce seems too thick, thin with a little milk.)
Serve immediately, or cover to keep warm until ready to serve, stirring occasionally.
Makes 1 cup