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1
Quick-soak beans by putting them in cold water to cover by 2 inches in a large pot. Bring to a boil, then boil 1 minute. Remove from heat and cover, then soak 1 hour. Drain, discarding liquid.
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2
Remove skin and bones from duck legs, reserving both, then coarsely shred meat.
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3
Heat oil in a large heavy pot over medium heat until it shimmers, then cook reserved bones, onions, carrots, celery, garlic, bay leaves, thyme, and cloves, stirring occasionally, until vegetables are softened, about 8 minutes.
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4
Add drained beans, broth, water, and tomatoes and simmer, partially covered, stirring and skimming froth occasionally, until beans are tender, about 50 minutes.
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5
Meanwhile, thinly slice reserved skin, then lightly season with salt and pepper. Cook in a dry medium nonstick skillet over low heat, stirring to separate, until fat is rendered and skin is crisp, 6 to 8 minutes.
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6
Discard bay leaves, bones, and thyme from soup. Transfer 2 cups solids and 1 cup liquid from soup to a blender and blend until smooth (use caution when blending hot liquids), then return to soup. Stir in 2 teaspoons salt and 1/2 teaspoon pepper and keep warm, covered.
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7
Heat Armagnac in a small saucepan over low heat just until warm, then carefully ignite with a kitchen match (use caution; flames will shoot up). When flames subside, stir Armagnac into soup along with meat, parsley, and salt and pepper to taste. Serve sprinkled with crisp skin.
