In a medium saucepan melt the butter over medium-high heat. Add the flour and cook, stirring constantly, until the roux is pale yellow and frothy, about 1 minute. Do not allow the roux to brown. Slowly whisk in the milk and continue to whisk until the sauce thickens and comes to a boil, about 2 to 3 minutes. Reduce the heat to a simmer and season with the salt, pepper and nutmeg. Allow to simmer for 2 to 3 minutes. This is now called a bechamel sauce, and may be used as is to top any number of dishes.
Stir in the cheese and whisk until melted. If the sauce seems to thick, thin with a little milk.
The sauce is now called a Mornay Sauce. Pour over steamed vegetables and serve immediately. If not using right away, cool, cover surface with plastic wrap and refrigerate for several days.