SOAK THE PORK BELLY OVERNIGHT in water, chilled. Remove from water and rinse. Place belly in a large pot with the thyme, bay leaf, and peppercorns. Add enough water to cover and bring to a boil. Reduce heat and add the onions, carrots, celery and garlic. Simmer until cooked, about 3 hours. Allow the pork to cool slightly in the liquid. Remove the pork and place between two trays with a weight on top. Chill. When cold, cut into cubes and fry on all sides.
FOR THE POLENTA, combine water, 10g of butter, and salt to taste in a pan. Bring to the boil. Add the polenta and whisk until smooth, cover and cook over low heat until soft, about 40 minutes. Mix in the remaining 10g of butter, parmesan, and season to taste. Spread on a tray lined with cling film and chill. Portion the polenta, spread the mascarpone on top and sprinkle with parmesan. Place under grill, and brown until golden.
PREPARE THE PIGEON LEGS by removing the thighbone and rolling the drumsticks in cling film to form ballotines. Poach for 2 minutes, and let cool. Remove cling film.
Then confit the legs by placing them into a small saucepan with the thyme, garlic, bay leaf, and duck fat. Cook slowly over low heat for about 30 minutes.
MAKE THE PIGEON SAUCE, by browning the pigeon carcases and wings in a pan. Remove the bones, reserve, and sweat out the shallots and garlic. Add the thyme, bay leaf and peppercorns and cook out, about 2-3 minutes. Deglaze the pan with some sherry vinegar and tip in the port. Reduce until thickened, and then pour in the stocks and place the bones back in. Bring to a boil, then reduce heat and let simmer for about 40 minutes. Strain through a fine chinois.
BROWN THE PIGEON in a saucepan until coloured on all sides. Baste with butter and cook until desired doneness. When rested, remove breasts from the crown and trim excess fat and cartilage.