Put the butter in a saucepan and put it on low heat. Melt the butter, avoiding boiling.
Pour flour into the butter. Start stirring immediately with a whisk. Without removing from heat and with continuous stirring, fry the flour mixture for a few seconds until a light nutty aroma.
Start adding the milk in several parts and continue stirring the sauce. Keep stirring until the sauce is smooth.
Add salt, pepper, and nutmeg to the sauce. Stir.
In some minutes, the sauce gets the needed consistency. The sauce is ready. It must be used almost immediately. Otherwise, milk foam will form on its surface. If you are preparing the sauce ahead of time, cover it with cling film, so it fits snugly on the surface.