Melt butter in a heavy-bottomed saucepan over medium-high heat. Stir in flour, and cook, stirring constantly, about 1 minute. (Do not let mixture brown.) Add milk, whisking constantly. Bring to a low boil, and cook, stirring constantly, about 2 minutes more. Season with salt, pepper, and nutmeg. Remove from heat, and stir in cheese. Use immediately.