In a large sauté pan, skillet or flat bottomed wok over medium-high, heat the extra virgin olive oil until hot, pat-dry the chicken thighs and add them to the pan, sauté for a few minutes each side until the skin starts to brown, then remove and set aside, and turn the heat down.
Scrape any chicken pieces from the bottom and sides of the pan, and to the same pan add the finely diced onion, carrot, and celery and sauté on low-medium heat until soft and fragrant, stirring frequently, to make a soffritto.
Add the minced garlic, salt and pepper, rosemary and bay leaves to the soffritto and continue to sauté for a few minutes until golden brown, taking care not to let it burn.
Pour in the red wine, stir for a couple of minutes, add the crushed tomatoes, half the can of tomato puree, stir to combine well, then return the chicken pieces, ensuring they’re fully immersed in the sauce.
Simmer on low for 15 minutes uncovered until the sauce starts to reduce, then cover and simmer, stirring every 10-15 minutes, for 30 minutes or so until the chicken has cooked and is tender, and the sauce has thickened. If the sauce reduces too much, add a little more tomato puree as needed. For an even more luscious sauce, cook up to an hour.
When the sauce is rich and shimmering and the chicken almost falling off the bone, taste and season with more salt and pepper if needed. If you’re adding olives, add them now, and simmer for another 5 minutes.
Plate the chicken, generously spooning the sauce over it until it’s swimming in the stuff, garnish with chopped fresh parsley and basil, sprinkle with grated Parmigiano Reggiano, and serve with slices of sourdough or another crusty bread to mop up the sauce.