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Cooking the duck legs in their own fat:
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Trim the excess skin and all the visible fat from the duck legs; cut the skin and fat into 1-inch pieces.
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Sprinkle 1/2 teaspoon of the salt on all sides of the legs.
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4
Pour 2 tablespoons of the oil into the pan, and set over medium heat.
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Arrange the legs in the pan, skin side down, and scatter all the skin and fat pieces in the spaces between them.
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As the fat starts to sizzle, lower the heat slightly and partially cover the skillet, leaving a gap of an inch or so for moisture to evaporate.
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Let the fat sizzle away, as you occasionally nudge and shift the leg pieces so they dont stick to the bottom.
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After 15 to 20 minutes, turn the legs overthe skin should be gold and lightly crisped already.
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Cook the legs on the flesh side for about 15 minutes, shifting them a bit, then turn them skin side down again and continue cooking for another 20 minutescook an hour altogetheruntil they are thoroughly crisp and deeply colored.
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Lift the leg pieces from the pan, letting fat drip off, and put them in a bowl.
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11
Carefully pour out the fat into a heat-proof container, but leave the crusty bits on the bottom and sides of the skillet.
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12
Flavoring and finishing the duck:
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Return the skillet to the stove; pour in 3 more tablespoons of olive oil, and set over medium heat.
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Stir in the garlic slices, and cook for a minute or two, until they start to sizzle.
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15
Drop the chopped anchovies in a hot spot; cook, stirring, for a minute or morethe anchovies will melt away in the oil.
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Now drop in the olives and stir them around, scraping up some of the browned bits in the pan as you do, for a minute or more, until theyre starting to cook.
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Put the duck legs back into the pan, toss in the branches of rosemary, and get the duck cooking again, turning the legs over in the oil and seasonings for a minute or two.
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18
When everything is hot, pour the red wine vinegar in several clear spaces around the pan; toss and stir everything as the vinegar steams and the acidity cooks off.
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After a minute, sprinkle on another 1/4 teaspoon of salt and pour in the wine, also on hot spots, and stir for a minute, then cover the pan completely.
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20
Cook covered for 4 or 5 minutes over low to medium heat, then uncover and turn everything well, coating the duck with the liquid and using it to deglaze the browned bits in the pan.
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21
Taste the sauce and add salt if necessary; drizzle over a tablespoon or two of olive oil if the sauce needs more viscosity.
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Cover the pan, and cook another 4 to 5 minutes.
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Uncover, and give everything a final stir so the duck is well coated with thick sauce and bits of olives.
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24
If there's loose, wet sauce in the pan, cook and stir until it is thickened.
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But if the duck is dry and there are stuck brown bits on the pan, pour in a bit of broth to loosen things up and get the duck moist and glistening with the sauce.
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26
Remove from the heat and serve.
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Let the duck rest in the pan, partially covered, if you want; refresh and reheat it with a bit of broth before serving.