Special equipment: Needle and thread, basting tube, thick string for noose
For the duck: Clean and eviscerate the duck, making as small an opening as possible. Rinse the duck inside and out. Pat dry with paper towels. With a large eyed needle and thread or thin string, sew up the cavity to make the duck air-tight. Insert a straw or basting tube into the hole at the neck. Blow up the duck to separate the skin from the flesh. The duck should blow up like a balloon. Immediately tie a noose around the neck. Once the duck is blown up, do not lay it down.
Meanwhile, bring 12 cups water to a boil in a large deep pot that can hold the duck. Add the sugar and stir to dissolve.
Dunk the prepared duck into the sweet water. You will see the pores and skin tighten. Be sure to dunk all the duck skin, using a ladle to spoon water over the duck if necessary. Remove and immediately hang to dry at room temperature. Ideally, this step should take 5 to 6 hours. When the duck skin feels like parchment, it is ready to roast.
Preheat the oven to 350 degrees F. To keep your oven clean, line a pan with aluminum foil and spread a layer of sand or unscented kitty litter thinly over it. Place on the bottom of the oven. This is to catch any dripping fat.
Place the duck, breast-side up, directly on the oven rack and roast until the duck is mahogany in color, 1 to 1 1/2 hours. Remove from the oven and immediately slice the skin off the duck. Serve the duck skin with the steamed yeast buns, cucumber matchsticks, scallion flowers and hoisin sauce.
For the stir-fry: Shred the duck meat. Combine the cubed ginger, chestnuts, tree ears, mushrooms and carrot in a bowl. Combine the bean sauce, wine, soy sauce, sesame oil and sugar in a small bowl.
Heat the vegetable oil in a wok over high heat. Add the minced ginger and half of the scallions and all of the vegetables. Stir fry for 1 minute, tossing to mix well. Add the duck meat and continue stir frying until the meat is heated through. Add 1/2 cup of the reserved mushroom water. Add the sauce, stir to blend and thicken with a little slurry so the sauce will cling to the meat mixture.
Sprinkle with the remaining scallions and serve.
A Confucian duck is non-eviscerated, which means its organs and innards have not been removed and therefore, the skin is more intact, as it hasn't been overly cut in a hasty cleaning process. (An uncut skin is easier to blow up and trap air.) If the duck is purchased already cleaned, make sure to tightly sew any openings in the skin while sewing the cavity.