Tip the chicken into a large bowl or dish and add the garlic, wine, 2 tbsp oil and the thyme. Season with 2 tbsp flaky salt and mix well until completely coated. Cover and chill for at least a few hours, but preferably overnight.
Heat grill to high. Arrange the plum tomatoes on a tray, cut-side up, drizzle with the remaining 1 tbsp oil and grill for 15 mins, or until charred. Set aside.
Heat 1 tbsp oil in a large casserole dish or flameproof roasting tin. Scrape the marinade off the chicken pieces back into the bowl and fry the chicken in batches for about 15 mins until the skin is golden and crisp – watch out, the oil has a tendency to sputter. Remove the chicken from the dish and pour off the oil. Place the dish back on the heat, add the tomato purée and cook for 2 mins, then add the herbs, fennel seeds, remaining marinade and chicken stock. Bring up to the boil, add the grilled tomatoes, then simmer gently for 20 mins.
Heat oven to 160C/140C fan/gas 4. Nestle the chicken pieces back into the dish, then stir them in to coat in the sauce. Scatter over the celery, button onions and artichokes. Bring up to a simmer, pop the lid on, then transfer to the oven and cook for 1 hr. Remove the lid and stir in the olives. Season to taste and leave everything to settle for 15 mins before serving straight from the dish.