In a small saucepan, add the milk, flour, salt, pepper (if using), and butter.
Bring the mixture in the saucepan up to a boil, and boil for 1 minute, stirring constantly. The mixture will thicken. (See video.)
After one minute, remove the saucepan from the heat.
Add the dry mustard (if using) to the mixture, and stir well to incorporate.
Add half the cheese to the mixture, and stir well until completely melted.
Add remaining cheese to the mixture, and stir well until completely melted.
You can now use your homemade cheese sauce.
To store, refrigerate the cheese sauce in a tightly-sealed container with a piece of plastic wrap placed over the cheese sauce to prevent the development of a "skin" on top of the sauce.
Refrigerated, the cheese sauce will stay fresh for up to 4 days.
You can freeze this cheese sauce but for no longer than 3 months. When ready to use, allow the sauce to thaw in the refrigerator and then warm in a saucepan on low heat.