Leaving the skin intact, remove the neck bone from the duck and reserve for later use. Fold the excess skin over the cavity openings on either end of the duck and sew securely shut with the twine. Cut a small "tracheotomy" slit just big enough for the nozzle of the air pump. Combine 1/2 cup of water with the honey, allspice, star anise, ginger and tangerine peels. Bring to a boil, then remove from the heat. Insert the nozzle and slowly pump air into the duck until it inflates and the skin pulls away from the meat. Baste with the honey glaze for several minutes. Hang the duck or prop upright in the refrigerator for 24 hours to dry.
Preheat the oven to 325 degrees F (300 degrees F if using convection). Remove the duck from the refrigerator and bring to room temperature.
Remove the strings from the duck and trim away excess neck skin. Split the duck in half from tip to tail. Place a rack over a roasting pan and add some boiling water to bottom of pan, but not touching the rack. Place the duck halves on the rack cut-side down and roast for 30 minutes. Remove the pan from the oven and rest for 15 minutes.
Turn the heat up on the oven to 450 degrees F.
Meanwhile, in a saucepan bring the neck bone and stock to a simmer for 15 minutes. Add the pine nuts and braise for 1 minute, then remove with a slotted spoon and set aside. Add the turnips to the stock and braise until tender, 30 minutes. Remove the turnips with a slotted spoon and set aside. Remove the stock from the heat and reserve.
While the turnips braise, pour out any liquid left in the duck roasting pan. Place the duck on a rack over the drained pan and roast to color and crisp skin, 15 to 20 minutes. Remove and rest the duck 15 minutes before serving.
In a medium skillet, heat the oil over medium-high heat. Add the blood oranges in a single layer and caramelize for about 1 minute per side, then remove and set aside. Deglaze the pan with white wine and add the green garlic, winter melon if using, braised pine nuts and salt. Add 1 cup of the stock and bring to a boil. Reduce the heat and simmer for 2 minutes. Set aside until ready to serve.
Carve the duck and arrange on a plate with the caramelized blood oranges and braised turnips. Spoon the sauce over the top and garnish with kumquat slices and chervil leaves.
NotesThis recipe was provided by a chef, restaurant or culinary professional and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.