Step 1Prepare the duck: Remove any excess fat in the body cavity near the rear opening. To refresh the duck, vigorously rub the salt into its cavity and on its skin. Rinse, drain and pat dry with paper towel.
Step 2Put the duck, breast side up, on a baking sheet. Sew up the duck's abdominal cavity with a bamboo skewer; break off the excess skewer, if you like.
Step 3To inflate the duck, use the tip of a paring knife to pierce a hole at the bottom of the duck's neck. Aim for the firm center just above the wishbone.
Step 4Inflate the duck, directing air to one side, then the other. The duck should puff up to reveal a six-pack abs-like structure. If the duck just puffs a little, then you may be pumping air into the cavity and not under the skin. Reposition the nozzle higher. If there is an air leak in the skin, make a new hole below the original one and retry. Flip the duck over and inflate its backside, making a hole at the top of the spine. Expect the duck to lose some air once you remove the pump nozzle.
Step 5Put the duck on a cutting board and use a heavy cleaver or knife to cut off its legs, right below the knee joint. Then cut off the first two joints of its wings. Finally cut off its neck, leaving about 2 inches attached to the body. Cut the head from the neck and discard. Refrigerate the remaining spare parts (neck bone, wing tips, feet) for the broth. Put the duck, breast side up, on a vertical roasting rack placed on a baking sheet and set near the stove.
Step 6In a saucepan, combine 3 cups water, two-thirds cup rice wine, honey, light soy sauce and 1 1/2 teaspoons of the dark soy sauce. Bring to a boil, then reduce the heat to maintain a good simmer.
Step 7Slowly ladle two-thirds of the mixture on the duck, bathing it from the top of its thighs to the top of its neck. Partway through, flip the duck over and repeat on its backside.
Step 8Now add the remaining 1 tablespoon of dark soy sauce to the leftover mixture, stir and ladle the liquid over the lower portion of the duck. It's OK if some of this darker liquid runs to the upper part.
Step 9Lift the duck off the rack and set aside briefly. Discard the pooled liquid and wash the rack and baking sheet. Replace the rack in the baking sheet, then put the duck on top, breast side up. Slide the duck into the refrigerator and let it air chill, uncovered, for 1 1/2 days, roughly 36 hours. Expect the skin to darken as it dries and to feel somewhat like parchment paper. (The mandarin pancakes can be made ahead of time while the duck dries.)
Step 10Return the dried duck to room temperature before roasting. Position a rack in the lower third or bottom of the oven to allow the duck to roast upright in the middle of the oven; the top of its neck should be about 3 inches from the broiler element. While the duck is warming, heat the oven to 450 degrees.
Step 11If needed, lightly spray or oil the vertical roaster. Turn and partially pull out the bamboo skewer to open the duck's body cavity about 3 inches. Insert the vertical roaster. It's OK if the duck is leaning forward or slouching a bit. Place the duck in a roasting pan, add a good quarter inch of water, then slide the pan into the oven.
Step 12Roast for 15 minutes, then lower the temperature to 350 degrees and continue roasting until the skin is crisp, richly browned and shiny, about 1 to 1 1/4 hours. Rotate the pan as needed so the skin browns evenly. When it is ready, the skin should sound hollow when gently tapped.
Step 13While the duck roasts, ready the accompaniments. To make the sauce, whisk together the bean sauce, remaining 2 teaspoons rice wine and remaining tablespoon water in a small bowl. Taste and add sugar, sesame oil or both as desired. The sauce is ready to use.
Step 14Put the green onions and cucumber on one or two plates. Place the sauce and vegetable garnishes on the table, and ready the steamer and mandarin pancakes for reheating.
Step 15When the duck is done, remove from the oven and set aside to rest for 10 to 15 minutes.
Step 16Twist and completely pull out the skewer. To remove the skin without it getting soggy, keep the duck on the roaster. Visualize the duck skin as four long quadrants. Now use a knife to cut downward through the skin, first to split the breast, then down the two sides and the back. Pry and peel away the large pieces of skin. You will have to make some additional horizontal cuts to remove the skin. Set the skin aside on a plate as you work.
Step 17Remove the vertical roaster from the skinless duck, and disassemble the carcass, cutting or pulling the flesh off the bones. Prepare to present the meat alongside the skin, setting aside 1 1/2 cups if desired to make the stir-fry recipe. (As the duck is broken down, save the carcass to add to the duck broth recipe if desired.) Reserve the 1 1/2 cups (one-half pound) of meat for the stir-fry and save the remainder to present alongside the skin.
Step 18Break up the carcass and add it to the soup, along with any leftover bits. Simmer the soup as directed.
Step 19To serve the duck with pancakes, cut the skin into pieces about 1 by 2 inches, and arrange on a platter. Include the duck meat. At the table, invite guests to take a pancake, smear on some sauce and top with a piece of skin, a piece of meat and a few green onion and cucumber strips. Fold or roll up the pancake and eat.