Melt the butter in a frying pan over medium-low heat.
Add the carrots and sauté for 2 minutes until slightly softened.
Add the onion, continue cooking for 2 minutes more, and add the celery.
Continue to sauté until all the vegetables are tender and just beginning to turn golden around the edges.
Season lightly with salt and pepper and remove from the heat.
Tips for Making This Recipe
Dicing the vegetables: It's important to dice the vegetables as uniformly as possible to ensure even cooking. The size of the dice can vary slightly according to the overall cooking time of the dish for which it is intended, e.g. the shorter the cooking time the smaller the dice.
Add the vegetables in the right order: Add the diced carrot to the pan first and cook until slightly softened before adding the onion. Cook until the onion begins to soften before adding the celery. Depending on the size of your dice, the total cooking time should be 10 to 12 minutes.
Be careful not to brown the vegetables: The concept behind preparing mirepoix is to slowly extract the mellow sweetness from the vegetables. Browning can impart bitterness and spoil the flavor.
Adding tomato paste: If desired, a small amount of tomato paste can be added when the vegetables are nearly finished cooking. This step is optional, but it's a nice enhancement if the mirepoix is being used in brown sauces or gravies.
Making a white mirepoix: If your mirepoix is being used in a white sauce or light gravy, chopped leeks can be used in place of the carrots.