In a saucepan over medium heat melt the butter. Add flour and cook for 2-3 minutes.
Gradually add milk and stir. The flour mixture will dissolve completely and the sauce will start to thicken. Cook for 2-3 minutes. Season with salt and pepper.
Remove from heat and add the cheese. Return the saucepan to the stove, lower the heat to the minimum and stir constantly, until the cheese melts. Add salt and pepper to taste. If the sauce looks too thick, you can add some more milk.
Reheating: Keep cheese sauce in the fridge for up to one week. Reheat on low in the microwave or in a saucepan over medium heat with some additional milk.