What is mirepoix and what purpose does it serve? Is it a type of cut such as julienne or Macedonia, or is it a type of cuisine?
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Mirepoix means 1: diced onions, carrots, celery and leek. 2. the type of cut of the mirepoix (see 1).
The dices are roughly cut about 1cm and don't have to be completely regular.
When talking about the cut, it should be about 1cm and regular. So you can cut potatoes in mirepoix, meaning 1cm cubes.
So, a cook can say, 'cut me a mirepoix' to mean roughly diced onions, etc.
And a cook can also say, 'cut me a potatoe in mirepoix' to mean evenly diced potatoes.
So, the answer is both. A cut and a combination.
Mirepoix, in every reference I've seen, refers to the chop of vegetables of onion, carrots, and celery - in the ratio of 2:1:1. You dice up the vegetables - normally small, but there are rarer applications (long stews for example) where a larger dice is acceptable, but certainly not the norm.
Mirepoix alone is not intended to be a dish - its a component that goes well with many, many other things. It has its roots in French cuisine and its generally a 'base' that you build other flavors upon. Think of it as "Here's a well known, good starting point to build complex flavors on". They are normally added to the dish very early on and often cooked at low heat in order to 'sweat', often with butter. In addition to their usage in normal dishes, they're included in stocks for the same reason. They provide good aroma and taste to the stock and sit well with other common meats and herbs.
Other cuisines have adapted a similar trio of veggies to use as a base. Cajun cuisine uses bell pepper in the place of carrots and calls it 'The Holy Trinity". Italian cuisine has the same principle in 'soffritto' - the principle difference being olive oil here, although it often contains garlic as well. In Spain, its sofrito - garlic, onions, and tomatoes - but it can also be more sauce-like.
A quick google revealed that it is neither a type of cut nor a type of cuisine, but rather the combination of onions, carrots, and celery that is used as basic flavoring in stocks and soups.