Add all the ingredients except salt and pepper to a deep frying pan.
Cook the mixture over medium heat, stirring constantly with a whisk until thick.
Season it with salt and pepper and it's done.
Addendum: since it's a pain washing the whisk, I use a fork instead when I make a small amount of sauce. It still comes out smooth.
You can change the thickness of the sauce by the amount of the milk, so it can be used in a variety of dishes, for example. Use less milk to make thicker white sauce for cream croquettes, or add more milk to make a cream soup.
Story Behind this Recipe
You can make this white sauce in no time. I add bacon and ketchup into leftover rice, and pour over white sauce to make an easy doria, or make a small amount of the sauce to make gratin with toasted bread, or use it in a bento box. Sometimes I add more milk to make a thinner sauce, and pour it over omurice as well.
The strength of gluten in the bread flour will easily produce a smooth sauce without fail, but you can produce good results with cake flour as well.