The stuffing takes a minimum of an hour, including cooling time, and is best done in advance. Put 4 tbsp olive oil to heat over a medium flame in a frying pan, add the livers and stir until coloured. Then add the diced potatoes, and cook until they are tender (you may need to add more oil, as the potatoes will stick, but don’t worry, simply scrape the crispy bits into the mixture). It is important that the potatoes are fully cooked. Coarsely chop half the fennel and add to the potatoes with half the olives. Mix thoroughly, season with salt and pepper, and set aside to cool.
Preheat the oven to 200°C/400°F/Gas 6.
Spoon the cool stuffing into the chicken. You will have quite a lot left. Rub the chicken all over with olive oil, and season very generously. Put the remaining stuffing in a suitably sized gratin dish with a little olive oil and set aside.
Put the chicken on its side into a casserole, and roast in the oven for 20 minutes, uncovered. It should be spitting and generally furious by this time. Gingerly turn the chicken on to the other side, and give it 20 minutes more; turn down the oven to 180°C/350°F/Gas 4 if it is browning too much. Put the excess stuffing into the oven to roast. Add the garlic cloves to the casserole and turn the chicken, breast side down, for 20 minutes. Turn it breast up, add the remaining fennel and olives and roast for a further 10–15 minutes.
Remove the fowl from the casserole to the chopping board and let it rest. Keep the garlic and olives warm in a dish. Remove any excess fat from the casserole. Add the wine to the casserole and boil vigorously until nearly evaporated. Add the broth and reduce by three-quarters. This whole process should take 10 minutes.
Cut the chicken into eighths, and arrange on a heated serving platter around the scooped-out stuffing. Scatter more chopped fennel, the olives and garlic on top, and serve with extra stuffing.