How to get a thick cheese sauce: The flour in the recipe acts as a thickening agent. If you just added flour to milk you’d end up with a clumpy mess. By combining the flour with a fat source (in this recipe it is melted butter), you will be able to distribute the thickening agent throughout the sauce without leaving clumps behind. This same principle can be applied to any sauce or soup that needs to be thickened. A roux is equal parts flour to fat. Cornstarch is a stronger thickening agent that I use (with butter) in things like puddings and cream pies.
