Roux (pronounced "roo") is one of the basic thickening agents in cooking. Used primarily for bulk up sauces and soups, roux is made from equal parts fat and flour. The "equal parts" are measured by weight, not volume.
Traditionally, a roux is made with clarified butter, which can be heated to a higher temperature without turning brown. If you're making a white sauce, you don't want to start off with brown butter. But you can certainly make a roux using ordinary whole butter; do not to let it burn when you're melting it.
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Stir in an Equal Amount of Flour
A given weight of butter will absorb an equal weight of flour. Clarified butter is pure butterfat, so you can use equal amounts of each. Whole butter, on the other hand, is 15% water, so you'll use a bit less flour.
For example, if you're melting half a stick of butter, which starts off as around 57 grams, assume 15 percent of the water is going to cook off, leaving about 48 grams. To get the precise amount, you'll have to weigh your flour. When the butter melts and turns frothy, it's because the water in the butter is starting to cook away. (Clarified butter doesn't have any water in it, so it won't froth.)
Slowly stir in the flour with either a wooden spoon or a whisk.
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Keep Cooking Until It's the Color You Want
As you continue to stir flour into the butter, you'll see that a thick paste is forming. You'll want to cook it for a few minutes because raw flour has a doughy taste you won't want in your sauce. Cooking the roux for a few minutes helps get rid of that raw flour flavor.
Beyond that, how long you cook the roux depends on what you're using it for. A béchamel sauce calls for a white roux, so you'll only want to cook it for a few minutes until the raw flour taste is gone but the roux is still a pale yellow.
A blond roux, used in white velouté sauces, needs to be a bit darker, so it's cooked a minute or two longer. A brown roux, used in brown sauces, is the darkest roux, and it's cooked for the longest amount of time. For that reason, you should cook it over a lower heat so that you don't burn it. Some cooks even brown the flour in the oven before adding it to the butter. Just remember that the roux's thickening properties are reduced as it gets darker.
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The Finished Roux
When you go to make your sauce or soup, it's possible to add the roux to the liquid you want to thicken. It's usually much easier to add the liquid to the roux. Whisk slowly as you add the liquid.
It's important that the roux is warm when you add your liquid. Too hot or too cold can both cause problems, leading to a lumpy result. The same goes for your liquid. Warm seems to work best, whether it's stock, milk, or anything else. If it's too cold it hardens the butter, and if it's too hot it can separate the roux.
The way roux thickens a liquid is by the starch molecules in the flour absorb the liquid and expand, becoming slightly gelatinous, which creates the effect of thickening the sauce. The fat helps to keep the starch molecules separate so that they don't clump up.
You can freeze roux and use it later. Try freezing it in ice cube trays and then transferring to freezer bags. You can even freeze it in muffin pans if you find ice cube trays too small.