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1
Put oven rack in middle position and preheat oven to 350F.
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2
Working from large cavity end, separate duck skin (including fat) from breast meat as much as possible by working your fingers between skin and meat, being careful not to tear skin, then prick skin all over ducks with a fork.
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3
Put ducks, breast sides up, side by side in a large flameproof roasting pan and rub each duck inside and out with kosher salt.
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4
Divide onions and celery between duck cavities and sprinkle 1/2 cup sugar around ducks.
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5
Pour enough boiling-hot water over ducks (to help tighten skin) to reach about halfway up ducks (don't fill roasting pan more than 1 inch from rim).
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6
Cover pan tightly with heavy-duty foil, then carefully transfer to oven and braise ducks 1 hour.
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7
Remove pan from oven and remove foil (do not discard), then carefully turn ducks over (breast sides down) using one large wooden spoon to turn and another inside cavity.
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8
Cover with foil, then carefully return to oven and braise until meat is very tender but not falling off the bone, about 1 hour more.
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9
Remove pan from oven and discard foil.
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10
Transfer ducks with wooden spoons to 2 large plates, draining any juices inside ducks back into pan, then transfer cooking liquid to a large bowl.
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11
Return ducks to roasting pan, breast sides up, and cool ducks and cooking liquid (separately), uncovered, then chill, uncovered, at least 4 hours (to firm up duck before roasting and to solidify fat on cooking liquid).
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12
Discard all fat from chilled cooking liquid.
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13
Remove zest from 2 large or 4 small clementines in strips with a vegetable peeler, then trim any white pith from zest with a sharp paring knife and cut zest into fine julienne strips.
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14
Blanch strips in a small saucepan of boiling water 5 minutes, then drain.
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15
Squeeze enough juice from remaining clementines to measure 2 cups and pour through a fine-mesh sieve into a 3-quart heavy saucepan.
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16
Add vinegar and remaining 2 tablespoons sugar and boil until reduced to about 1/3 cup (glaze will bubble up and darken), about 15 minutes.
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17
Reserve 1 tablespoon glaze in a cup to brush on ducks, then stir julienned zest and 1 cup cooking liquid into glaze remaining in pan and reserve for sauce.
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18
Reserve remaining cooking liquid.
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19
Put oven rack in middle position and preheat oven to 500F.
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20
Roast ducks until skin is crisp, 25 to 35 minutes.
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21
Brush reserved glaze (from cup) on ducks, then transfer ducks to a platter and let stand while finishing sauce, at least 10 minutes.
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22
Pour off all but 1 tablespoon fat from roasting pan and straddle pan over 2 burners.
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23
Add shallot and cook over moderately low heat, stirring, until softened and pale golden, 3 to 5 minutes.
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24
Add 2 cups reserved cooking liquid and deglaze pan by boiling, scraping up brown bits, 2 minutes, then pour through fine-mesh sieve into sauce (containing julienned zest) and bring to a boil.
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25
Stir together liqueur and arrowroot and whisk into sauce.
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26
Simmer, whisking occasionally, until thickened, 3 to 5 minutes, then season sauce with salt and pepper.
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27
Serve ducks, whole or carved into serving pieces, with sauce.
