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1
Gently prick the duck skin all over with a sharp paring knife (without piercing the meat) and place it on a rack set in the sink.
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2
Bring a small pot of water to a boil.
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3
Slowly pour the water all over the duck to render some of the fat; tilt the duck to drain the cavity.
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4
Transfer the rack with the duck to a baking sheet; pat the duck dry with paper towels.
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5
In a small bowl, combine the thyme, allspice, garlic powder, black pepper, crushed red pepper, onion powder and sugar.
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6
Rub the spice mix inside the cavity and all over the duck.
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7
Refrigerate uncovered for 1 to 2 days.
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8
Preheat the oven to 300.
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9
Season the duck with salt and stuff the cavity with half of the carrots and garlic.
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10
Transfer the duck to a rack (preferably V-shaped) set in a roasting pan and add the onion, chicken stock and the remaining carrots and garlic to the pan.
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11
Roast the duck for about 1 hour, until lightly golden and an instant-read thermometer inserted in the thickest part of the thigh registers 140.
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12
Increase the oven temperature to 450 and roast for 15 minutes longer, until the skin is deep golden and crispy and an instant-read thermometer inserted in the thickest part of the thigh registers 160.
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13
Let the duck rest for 20 minutes.
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14
Tilt the duck to release the juices into the roasting pan, then strain the pan juices into a medium saucepan and degrease with a spoon.
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15
Bring to a boil.
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16
Whisk in the butter and simmer for 5 minutes, until slightly thickened.
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17
Stir in the parsley and season with salt and pepper.
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18
Carve the duck and serve with the pan sauce.
