01 - Preheat oven to 340°F (170°C). Position the rack in the lower third of the oven for even heat distribution.
02 - Pat the duck pieces thoroughly dry with paper towels. Season generously on all sides with kosher salt and black pepper.
03 - Place a large Dutch oven over medium heat. Sear the duck pieces skin-side down for 5 to 7 minutes until deeply browned and fat has rendered. Flip and brown the opposite side for 2 to 3 minutes. Transfer to a plate and set aside.
04 - Pour off all but 2 tablespoons of rendered duck fat from the pan. Add the sliced shallots, smashed garlic, and leeks. Sauté until fragrant and softened, about 3 minutes.
05 - Add the carrots, parsnips, halved potatoes, and mushrooms. Stir for 2 to 3 minutes, coating the vegetables evenly in the rendered fat.
06 - Deglaze the pan with white wine, scraping up all browned bits from the bottom. Pour in the chicken stock, soy sauce, and honey. Drop in the bay leaves and thyme sprigs. Stir to combine.
07 - Nestle the browned duck pieces on top of the vegetables, skin side up. Bring the liquid to a simmer on the stovetop, then cover with the lid.
08 - Transfer the covered Dutch oven to the preheated oven. Braise for 1 hour 30 minutes, or until the duck is fork-tender and the vegetables are soft.
09 - Remove the lid and increase the oven temperature to 425°F (220°C). Brush the duck skin with neutral oil. Roast uncovered for 15 to 20 minutes until the skin is deeply golden and crackling crisp.
10 - Remove from the oven and let rest for 5 minutes. Discard the bay leaves and thyme stems. Serve the duck over the braised vegetables, spooning the braising juices around the plate.