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. Stir in cheese until melted.
Stir about 1/2 cup of the hot sauce into egg yolks; return to saucepan mixture, stirring until smooth and thoroughly heated. Season with salt, pepper, and Worcestershire sauce to taste.
Makes about 2 1/2 cups of medium thick sauce