Heat the butter in a 3- or 4-cup saucepan and when butter is melted add the flour. Stir with a wire whisk and when blended add the liquid, stirring vigorously and constantly. Add the salt, pepper, nutmeg, and cayenne.
Cook, stirring occasionally, for about 5 minutes or longer.
Remove the sauce from the heat and stir in the grated cheese. Serve hot over cooked cauliflower, asparagus, or other suitable vegetables.