In a heavy saucepan, melt the butter. Sprinkle the flour over it and stir to incorporate. Cook over medium-low heat for 2-3 minutes, whisking constantly.Slowly whisk in milk. Add cheese and stir until melted.
For Broccoli Cheese soup, add broccoli. Of course, if it's fresh broccoli, you'll want to cook it first. If it's frozen, you'll want to thaw, rinse and drain it before adding it to finished cheese soup and heating to desired temperature.