add the egg and cheese.

Melt butter in a saucepan, add flour. Stir on medium heat until the mixture is golden brown (5-7 minutes). Remove pan from heat, add milk (all together). Put pan back on the stove and bring to boil, stirring frequently. The sauce will thicken all of a sudden, as soon as boiling point is reached. Simmer 3-5 minutes, then remove from heat. Add salt, pepper, nutmeg.

This is the "base" sauce. It keeps well in the refrigerator for at least 4 days (just put plastic film directly on the surface, so it doesn't "dry up"); it can be heated up and served on boiled vegetables, meats etc.