Mirepoix is a combination of aromatic vegetables that gives a subtle background flavor to dishes such as soups, stews, and braises.
To make mirepoix: Rinse, trim, and peel vegetables -- typically two parts onion to one part carrot and one part celery -- then chop them into uniform pieces. The shorter the cooking time of your recipe, the smaller the pieces should be, so that they effectively infuse the foods with flavor.
You can add the mirepoix uncooked to stocks and broths for a light dose of flavor. To add richness to heartier stews and braises, "sweat" the vegetables first, cooking them with a little oil or butter over low heat until they start to release their juices into the pan.
Mirepoix, a French term, is only one of many possible variations. The Italian soffritto, like mirepoix, calls for onions, celery, and carrots, and sometimes pancetta and garlic. Mushrooms, parsnips, leeks, peppers, tomatoes, and garlic are all considered aromatic vegetables, and can be used in endless combinations.
The "holy trinity" includes onions, celery, and -- instead of carrot -- a bell pepper. This is used as a base of most soups and stews made in Louisiana, including gumbo. Green peppers were substituted because they're easier to grow in southern Louisiana.