Cheddar Brocolli Soup with a base of Cheese Sauce (made with White/Béchamel Sauce)

This Broccoli Cheddar Soup starts with white sauce to which you just add cheddar & broccoli. :0)

The BEST White sauce or Béchamel sauce:
(from "The Joy of Cooking")

Very Basic: used not only for creaming foods like vegetables and fish but as a base for many other sauces.

Melt over low heat:
2 tbsp butter
For a delicate flavour, even commercial establishments have found no substitute for butter. Add and blend over low heat for 3-5 minutes:
1 1/2 to 2 tbsp flour
Stir in slowly:
1 cup milk
[For better consistency, you may scald the milk beforehand; but be sure--to avoid lumping--that the roux (flour & butter mixture) is cool when you add it. ]

Add:
1 small onion studded with 2/3 whole cloves 1/2 small bay leaf
Cook & stir the sauce with a wire whisk or wooden spoon until thickened and smooth. Place in a 350 degree oven for 20 minutes to cook slowly. (The oven interval also saves your time and hands for other kitchen jobs.) Strain the sauce.
Season to taste.
When I'm making cheese sauce, I add V.E. Giardino salt blend & four pepper blend. A grating of whole nutmeg, a sprinkle of paprika, 1/4 tsp dry mustard, and the tiniest pinch of Cayenne.

[For creamed dishes, use about 1/2 as much sauce as solids.]

Cheese sauce:

Prepare White/Béchamel Sauce
When it is smooth & hot, reduce the heat & add:
1 cup or less (or more) ;0) grated cheese
Stir the sauce until cheese is melted.

To make this into Broccoli Cheddar Soup, just add an extra cup of milk & gently steamed broccoli that has been diced. It's also great with Chinese Broccoli, Cauliflower, or Spinach.