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1
Tie the spices in cheesecloth, set aside.
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2
Heat a stock pot with 1 tablespoon of the butter and the oil. Add the chicken wings and livers (or neck and giblets, if using), and cook, stirring often, until they begin to brown.
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3
Add the minced onions, and cook for 5-10 minutes more. Stir in the flour. Add the broth, the wine, the vermouth, the spice bag, and the tomato paste. Season with salt and pepper, and simmer gently, for about 2 hours, skimming the scum, from time to time.
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4
Bring a 6-cup saucepan, half-filled with unsalted water to a boil. Cook the olives 2 minutes, then drain, and rinse under cold water.
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5
Strain the sauce through a fine large sieve into another saucepan, of suitable dimensions and add the olives, discarding the solids, and spices, from the sieve. Simmer gently for an hour or more, until the sauce coats a spoon.
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6
Preheat the oven to 475 degrees, while the sauce cooks.
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7
Wash the duck, discarding (or reserving) any lumps of fat.
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8
Score the skin all over with a small sharp knife, rub with the remaining butter, and season the cavity, and flesh with salt and pepper. Tie the legs.
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9
Fit a roasting tin with a rack, put on the breast side down of the duck, and roast 20 minutes, basting. Flip, roast 20 minutes more, basting.
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10
Reduce thermostat to 350 degrees and roast until the duck registers 160 degrees (about 1 hour).
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11
Rest 20 minutes, then cut into pieces, as for chicken, and serve with the sauce all over.
