Preparation time: 30 minutes
Soaking time: 30 minutes
Cooking time: 2 hours 5 minutes
Preheat the oven to 163 °C (325 °F).
Place the dried mushrooms in a bowl and cover with warm water. Leave to soak for 30 minutes. Drain, then pat dry with paper towel.
Meanwhile, lay the duck flat on a cutting board, back side up. Remove the wishbone by scraping the bone near the breasts, then pull with your fingers to remove it. Cut the skin on the inside of the thighs, then dislocate the thighs at the joint. Cut at the joint to loosen the thighs. Cut the wings off at the shoulder joint. Cut along the base of each breast following the spine and rib cage to remove the breasts.
Season the duck with salt and pepper.
In a large saucepan, heat the duck fat over medium heat. Brown the duck breasts, thighs, and wings in batches for 4 to 5 minutes, turning the duck pieces a few times during cooking. Set aside on a plate.
In the same saucepan, sauté the mushrooms, stirring occasionally, 5 to 7 minutes, until the water has evaporated. Set aside on a plate.
In the same saucepan, cook the shallots, carrots, celery and garlic for 2 to 3 minutes. Season with salt and pepper.
Sprinkle with flour and continue cooking for 1 minute, stirring.
Add the red wine and simmer until half of the liquid has evaporated.
Add the veal stock, butternut squash, thyme, rosemary, bay leaf, barley, duck pieces and mushrooms. Bring to a boil, then cover and bake for 1 hour 45 minutes to 2 hours 15 minutes.
When ready to serve, add the parsley.