Sofrito is to Italian cuisine what mirepoix is to French cuisine. In fact a similar word, sofrito, is the word for another trinity product, usually including a forth ingredient, tomato product, in Spanish cuisine.
Recipes vary slightly depending upon the region of the country, but typically all terms refer to a combination of ingredients that are aromatic, in a particular ratio, usually small to fine dice, and used for a foundation or starting point for many cooked recipes all cuisines.
It is futile to memorize all but the mirepoix, because in American restaurant kitchens, the word mirepoix is well know to mean, 1 part carrot, 1 part celery to 2 parts onion. The chef simple tells her cooks the amount of mirepoix needed rather than listing each individual ingredient.
The Tuscan sofrito is a stew-like marriage of garlic, onion, carrot and celery. We often substitute fennel for celery for our sofrito, and omit the garlic, but only rarely. What sticks out to us is that for each application, the sofritto is well developed. In fact the flavors are well blended through a slow and careful saute with a little EVOO until mixture turns a rich deep color, becoming darker and darker the longer it is cooked. How long it cooks depends on the taste that the final dish requires.
In the Spanish version we typically add a tomato product like a paste or re-hydrated dried tomato, to celery, carrot and onion. Again, the amount of cooking and the amount of each ingredient and the size of the chop all varies according to final use.
There is even a version of this that is not used in cooking at all but rather as a condiment at the table. In this format it reminds us of a gremolata served with veal and lamb dishes.
In Cajun or Creole cooking the combination that forms the foundation of the recipe is referred to as the “holy trinity.” No disrespect intended, it is a way to convey that chefs of these cuisines “religiously” add the blend to their dishes. Green peppers are usually part of the holy trinity for these cuisines.