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1
Trim the excess fat from duck legs. Several hours ahead or the night before, season with salt and pepper. Cover and refrigerate.
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2
Preheat the oven to 425u00b0F.
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3
In an ovenproof skillet just large enough to hold the duck legs comfortably, heat the olive oil. Add the leeks and carrot. Cook over medium heat for 3 minutes. Stir in additional salt, thyme, parsley sprigs, bay leaf, and olives. Cook for 3 more minutes. Place the duck legs in the skillet, skin side down. Add to the skillet white wine and chicken broth with lemon zest.
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4
The liquid should be about 1 inch deep; add more liquid if needed. Raise the heat, bring to a simmer, and immediately put the skillet in the oven. After 30 minutes, take the pan from the oven and turn the legs skin side up. If necessary, pour off and reserve some of the liquid so that all the duck skin is exposed. Turn the oven down to 325u00b0F and continue cooking for 1 to 1 1/2 hours more. The duck is done when the skin is browned and the tip of a knife slips easily in and out of the meat.
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5
Set the duck legs aside and pour the braising juices and vegetables into a small bowl. Allow the liquid to settle, then skim off and discard the fat. The duck legs will render a surprising amount of fat. Taste for salt and correct the seasoning if needed. If it's too thin, reduce the braising liquid to concentrate it. Pour the liquid and vegetables back into the skillet with the duck legs on top. Just before serving, return to a simmer and reheat for a few minutes.
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6
Pitted olives can be substituted, but use fewer, about 1/2 cup, and don't add them to the braise until the last 15 minutes of cooking.
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7
Substitute dry sherry for half the wine.
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8
Substitute dried fruit such as prunes or figs for the olives. Use red wine instead of white and add a piece of bacon or pancetta to the braise. Omit the lemon zest.
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9
Substitute chicken legs for the duck legs. Reduce the cooking time by 30 minutes.
