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1
Heat a 12-inch skillet over medium heat. Season duck with salt and pepper. Cook skin side down, then turn, until duck is evenly browned (12-15 minutes), reserve fat for another purpose, or discard. Transfer duck to a plate and set aside. Heat oven to 350 degrees.
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2
Using a Dutch oven, with a heat resistant lid, a 12-inch saute pan, or a roaster, that can be covered in aluminum foil, put the broth, vinegar, 1/2 cup soy sauce, coriander seeds, 1 chile (chopped or whole), and the 1 cup of water. Add the duck legs, skin side up, cover, and put in oven to braise until tender, about 90 minutes. Gently remove duck to a plate when done, discarding cooking liquid, (the mixture may be cooled and frozen, if making this dish again).
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3
Make the sauce in a 4-cup pan by boiling the remaining soy sauce, garlic, ginger, sugar, sesame seeds, sesame oil, mustard, and chopped scallion, do not reduce, remove from heat, set aside.
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4
Boil the noodles in lightly salted water for 2-3 minutes. Drain, toss with 1 tablespoon oil, set aside.
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5
Heat a skillet with 2 more tablespoons oil, add remaining chilies (chopped or whole), mushrooms, and cabbage leaves, stir fry until cabbage leaves wilt, 5-7 minutes.
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6
Add noodles, and 1/2 cup of the reserved sauce, stir, cover to keep warm.
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7
Over medium-high heat, heat remaining 2 tablespoons oil in a skillet, and fry duck, skin side down, for 4 minutes, or until crisp. Remove from heat, turn duck. Brush with remaining sauce.
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8
Place servings of warm noodles onto warm plates, and put one serving of duck, over each. Serve at once.