01 - Preheat oven to 340°F.
02 - Pat the duck pieces thoroughly dry with paper towels. Season all over with kosher salt and black pepper.
03 - In a large Dutch oven or deep ovenproof skillet over medium heat, sear the duck pieces skin-side down for 5–7 minutes until deeply browned and fat renders out. Flip and brown the other side for 2–3 minutes. Remove and set aside.
04 - Pour off all but 2 tablespoons of duck fat from the pan. Add the shallots, garlic, and leeks. Sauté until fragrant and softened, about 3 minutes.
05 - Add carrots, parsnips, potatoes, and mushrooms. Stir for 2–3 minutes to coat evenly in the rendered fat.
06 - Deglaze the pan with white wine, scraping up any browned bits from the bottom. Add chicken stock, soy sauce, honey, bay leaves, and thyme. Stir to combine.
07 - Nestle the browned duck pieces skin-side up on top of the vegetables. Bring to a simmer on the stovetop, then cover with a lid.
08 - Transfer the covered vessel to the oven and braise for 1 hour 30 minutes, or until the duck is tender and the vegetables are soft.
09 - Remove the lid, increase oven temperature to 425°F, and brush the duck skin with neutral oil. Roast uncovered for 15–20 minutes until the skin is crisp and golden.
10 - Remove from the oven and let rest for 5 minutes. Discard bay leaves and thyme stems. Serve the duck over the vegetables with braising juices spooned around.