1, In a large, deep stockpot, whisk together 4 quarts cold water, 1 cup of the brown sugar, and the salt until the sugar and salt have dissolved. Set aside.
2, In a heavy sauté pan, toast the cinnamon, star anise, cloves, and Sichuan peppercorns over medium heat, shaking the pan frequently, for about 2 minutes, until the spices are aromatic. Add the toasted spices to the water–brown sugar mixture. Immerse the duck in the brine, top with a weighted plate to keep the duck submerged, cover, and refrigerate overnight.
3, Remove the duck from the brine, discard the brine, and wipe away any spices clinging to the duck. Place a roasting pan over two burners on the stove top and pour in water to a depth of 2 inches. Turn on both burners to medium-high heat and set a V-shaped roasting rack in the pan. Put the duck, breast side up, on the rack and cover the roasting pan tightly with aluminum foil. Steam the duck for 30 minutes, checking periodically to ensure water remains in the pan and adding hot water if needed.
4, When the duck has almost finished steaming, prepare an ice bath. In the stockpot, whisk together 4 quarts water and the remaining 1 cup brown sugar until the sugar has dissolved. Add the ice cubes.
5, When the duck has steamed for 30 minutes, remove it from the roasting rack and immediately plunge it into the waiting ice bath. Let chill for 5 minutes. Meanwhile, set a wire rack on a rimmed baking sheet. When the 5 minutes have passed, transfer the duck, breast side up, to the wire rack and refrigerate uncovered, for at least 4 hours or up to overnight.
6, Pour the oil into a large, deep stockpot and heat over high heat to 350°F on a deep-frying thermometer. Line a baking sheet with paper towels and place near the stove. When the oil is ready, carefully lower the duck into the oil, releasing a leg at the last minute so that the oil doesn’t splash, and fry for 12 minutes. Using a spider, carefully transfer the duck to the paper towel–lined baking sheet and let stand 15 minutes.
7, Over high heat, reheat the oil to 375°F. Line a second rimmed baking sheet with paper towels. When the oil is ready, again carefully lower the duck into the oil and fry for 1 to 2 minutes, until the skin is well bronzed and crispy. Using the spider, transfer the duck to the fresh paper towels to drain for a few minutes.
8, Place the duck, breast side down, on a cutting board. Using poultry shears, cut the backbone from the duck. Then, using a heavy cleaver, chop the duck through the bone into bite-size pieces (see How to Chop a Whole Bird, Asian-Style for directions).
9, Arrange the watercress on a serving platter and top with the duck pieces. Serve immediately.