If you have ever made soup from scratch, there is a high chance that you have made a mirepoix, even if you didn't know it. The basis of many different dishes, a mirepoix (pronounced meer-PWAH) consists of carrots, onions and celery. The three veggies are lightly cooked in oil or butter until they soften and release their aromas before adding other ingredients and before they begin to brown.
Although a mirepoix is a French staple, many different cuisines have their own versions that serve the same purpose. This includes the Spanish sofrito (made with tomatoes, onions, garlic and bell peppers) and the Cajun holy trinity (onion, green bell pepper, and celery).
The ratio for mirepoix can vary between recipes but the common one is 2:1:1 of onion, carrot and celery. Chop your vegetables roughly into similar size, then add them to a pan on medium-low heat with oil or butter and cook until aromatic. If you are using your mirepoix for a meat dish, sear the meat first so you can cook the mirepoix in the fat and browned bits for more flavour.