From The Cook's Bible:
How to Thicken a Sauce

by Christopher Kimball

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To make a sauce or a base for a soufflé, for example, hot milk, cream, or stock is added and, in just a few minutes, the liquid thickens up nicely. The thickness of the sauce is easily varied by changing the proportion of roux to liquid. For a thinner sauce, a French chef uses 1 tablespoon each of butter and flour to 1 cup of liquid; for a medium sauce, 2 tablespoons each; for a thick sauce, 3 tablespoons. These two basic sauces, a béchamel and a velouté, are the basis for classic French white sauces.

By adding additional ingredients, such as cream, cheese-flavored butters, herbs, tomatoes, egg yolks, curry, white wine, lemon, onions, peppers, etc., or combinations thereof, chefs made more than 20 different sauces, everything from an aurore sauce (with tomato purée) to a Mornay sauce (with cheese). Although these two mother sauces are important as ingredients in recipes, I find them relatively useless for sauces. They are too heavy, too thick, and too high in fat. You do need, however, a béchamel for a soufflé, and a béchamel or velouté is also used in a classic lasagna, along with a basic tomato sauce.

Recipe for Mushroom Purée
You can add a mushroom purée to almost any sauce.

4 cups mushrooms, rinsed and quartered
1/4 cup chicken or beef stock, preferably homemade
1/4 cup white wine
1 tablespoon butter
1 teaspoon lemon juice
1/2 teaspoon white wine vinegar

1. Purée the mushrooms with stock and wine in a blender or food processor. Add all ingredients to a saucepan and simmer until all moisture disappears.

Christopher Kimball is the founder, publisher, and editor of Cook's Illustrated magazine, and the author of The Cook's Bible and The Yellow Farmhouse Cookbook .