Place the duck, skin-side down, in a cold frying pan. Turn the heat onto medium and cook for 8-10 minutes or until the skin is well browned and the fat has begun to render. Set them aside on a plate and drain off excess fat, leaving a little of the duck fat in the pan.
Sauté the celery, onion, carrot and garlic, stir occasionally for 6-8 minutes until the vegetables have begin to soften. Add the red wine and vinegar, simmer for 3-4 minutes until slightly reduced and add the tomato purée, chopped tomatoes and the chicken stock along with the duck legs. Bring to the boil, reduce the heat, cover and simmer for 1.5 hours until the duck is tender.
Once the duck is almost cooked place a pot of salted water over a high heat, once boiling add the pappardelle and cook according to packet instructions.
Remove the duck legs to a plate, bring the sauce to a boil and simmer for 15-20 minutes until slightly reduced. Shred the meat off bones, discarding any skin and bones, return the meat to pot, tossing through the sauce. Toss the pasta through the duck ragu, leaving a little duck behind to garnish. Serve in bowls topped with some of the remaining duck and shavings of pecorino.