Sauces are jewelry of the kitchen wardrobe. But a sauce isn't usually very useful unless it is thick enough to cling to the food, and so it is necessary to thicken most sauces in some way. Here's a rundown of ways to do this, and keep in mind it works to thicken other things, too.
1. Starch powder: The most obvious method is to use a powdered starch like flour. Cornstarch, arrowroot, and tapioca all work, too, the main difference being that flour is cloudy whereas those other three are clear.
To thicken with starch, you must whisk the starch into a cool liquid, you cannot whisk it into a hot liquid or it will clump.
Alternatively, you can make a paste (also called a roux) using the flour and a small amount of either melted fat or water, and gradually, carefully whisk the rest of the liquid in a bit at a time. This is ideal when you want to cook the flour a little to make it develop flavor, but is not recommended for other starches.
One last way to incorporate it is to sprinkle it atop dry vegetables or meats while they are sauteeing. The flour clings to the veggies instead of clumping, and you can add the rest of the liquid all at once without worry.
Advantages: Readily available, foolproof if you follow directions
Disadvantages: Adds little or no flavor, adds carbs
Additional properties: Flour-thickened sauces get thicker as they cool, but cornstarch-thickened sauces tend to get thinner. Very stable once cooked and won't curdle, but might scorch.
2. Egg: Eggs, either whole or just the yolk, thicken any liquid into a rich and silky custard. The obvious use is for ice cream and custard sauce, but eggs can also be used to thicken mustard sauce and wine sauce to excellent effect.
The big problem is overcooking and curdling. Avoid this by heating the liquid to a boil, and then gradually whisking the liquid into the eggs (in a separate bowl), not the other way around. If necessary, return to the heat and cook a little longer, but stop instantly if the liquid begins to look clumpy. To rescue a clumpy sauce, put it into the blender and puree. It will be thinner but the clumps will go away.
Advantages: Delicious flavor and richness, adds nutrition
Disadvantages: Adds fat and cholesterol, adds allergens (eggs are allergenic), easy to mess up
Additional properties: Tends to gel slightly while it cools. Unstable, may curdle easily.
3. Onions: Onions will cook down into a pulp when simmered for a long time. This is most useful in stews. Use enough onions, and you will not need to thicken your stew with flour at all; it will make a delicious thick broth on its own.
Advantages: Extremely flavorful, healthy (it's a veggie!), non-allergenic for most people
Disadvantages: Takes a long time, not practical for anything but stew and tagine
Additional properties: Very stable. Won't curdle or change texture.
4. Pureed vegetables: Many cooked veggies can be pureed and added to sauces, or used as a sauce. The best are carrots, cauliflower, potatoes, and coconut milk (which is pureed coconut).
