This is a variation on Bechamel Sauce, turning the white sauce into a cheese sauce. It's based off of the Bechamel Sauce recipe from Mastering the Art of French Cooking, by Julia Child and Simone Beck.
--A NOTE ON EQUIPMENT: The recipe actually calls for a heavy-bottomed, 6-cup enameled, stainless steel, lined copper, porcelain, or pyrex saucepan and the use of a wire whisk for mixing. If you use anything with a non-stick coating, use a nylon whisk instead. A thin-bottomed pan is a poor heat conductor and may cause the sauce to scorch. Aluminum can discolor a white sauce.
--2 tbsp Butter
--2 tbsp Flour
--2 cups Whole Milk, brought to a boil with 1/4 tsp Salt
--Pinch of Nutmeg
--1/2 cup of Grated Cheese (any cheese can work, but the classic is Swiss Gruyere or a Swiss Gruyere/Parmesan Blend)
In saucepan, melt the butter over low heat. Blend in the flour, and cook slowly, stirring, until the butter and flour froth together for 2 minutes without coloring. This is now a white roux. Remove the roux from the heat. As soon as the roux has stopped bubbling, pour in all of the nearly-boiling milk at once. Immediately beat vigorously with a whisk to blend liquid and roux, gathering in all bits of roux from the inside edges of the pan. Set saucepan over moderately high heat and whisk until the sauce comes to the boil. Boil for 1 minute, stirring. Remove from heat, and beat in salt, pepper and nutmeg to taste. Let sauce cool for several minutes, then stir in cheese. If the sauce gets stringy or clumpy, whisk in several drops of lemon juice or dry white wine while heating sauce over medium heat.