Melt butter in a saucepan over medium heat. Add flour and stir until mixture is well blended. Gradually stir in hot milk. Cook over medium heat, stirring constantly, until sauce begins to boil and thickens. Simmer, stirring frequently, over very low heat for 5 minutes. Season with salt and pepper to taste and add a little nutmeg, if desire.
Add 1/2 cup grated cheese to 1 cup of hot sauce; stir over low heat until cheese is melted. Season with a little mustard or Worcestershire sauce to taste.
Substitute chicken, beef, fish, or vegetable broth for the milk.
Add 1 teaspoon of freshly chopped herbs or 1/2 teaspoon dried herbs to 1 cup of hot sauce. Cook for a minute or two longer to get more flavor from the herbs.
Add 2 or 3 tablespoons of heavy cream to the finished sauce. For an onion flavor, add an onion slice to the milk when heating; remove onion slice before adding milk to flour and butter mixture.
Combine 1 teaspoon dry mustard to flour used in sauce. This sauce is especially good with fish and chicken.