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1
Break up tamarind, then add to boiling-hot water (1/2 cup) in a heatproof bowl and soak 15 minutes. Mash tamarind with a fork until pulp is dissolved, then pour tamarind mixture through a fine-mesh sieve into a small bowl, pressing hard on solids to extract as much liquid as possible. Discard solids.
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2
Heat a dry 10-inch heavy skillet (preferably cast-iron) over moderately low heat until hot, about 2 minutes, then toast coriander and cumin seeds, stirring constantly, 2 minutes. Add 12 curry leaves and toast, stirring constantly, until leaves curl and darken, 3 to 4 minutes. Add 4 chiles and toast, stirring constantly, until a shade darker, 1 to 2 minutes. Transfer to a plate and cool completely, then finely grind in grinder.
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3
Pat chicken dry and sprinkle with 1 teaspoon salt. Heat 2 tablespoons oil in a wide 6-quart heavy pot over moderately high heat until hot but not smoking, then brown chicken in 2 batches, skin sides down first, turning over once, about 8 minutes per batch. Transfer to a plate.
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4
Pour off all but 2 tablespoons fat from pot, then cook onions over moderate heat, stirring occasionally, until edges are golden, 5 to 8 minutes. Reduce heat to moderately low, then add ground-spice mixture, garlic, turmeric, and remaining teaspoon salt and cook, stirring frequently (to prevent scorching), about 3 minutes. Add coconut milk and tamarind liquid and simmer, stirring, until any coconut-milk solids are dissolved, about 1 minute. Add chicken, skin sides up, in 1 layer (chicken will not be completely covered with liquid) and simmer, covered, until chicken is just cooked through, about 15 minutes.
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5
While chicken simmers, cook green beans in an 8-quart pot of boiling salted water until crisp-tender, 3 to 4 minutes. Drain and transfer to a bowl of ice water to stop cooking. Drain well.
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6
When chicken is done cooking, transfer with tongs to a cutting board, reserving sauce in pot, and halve each chicken breast diagonally through bone. Put chicken in a deep serving dish and keep warm, covered with foil. Add green beans to coconut sauce and simmer until just tender, about 1 minute.
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7
While beans simmer, heat remaining tablespoon oil in 10-inch heavy skillet over moderate heat until hot but not smoking. Add mustard seeds, then cover skillet and cook until seeds make popping sounds, about 5 seconds. Remove lid, then add remaining 15 curry leaves and 2 chiles and cook, stirring, until leaves crackle and chiles darken slightly, about 5 seconds. Pour hot oil mixture over coconut sauce and beans, then stir to combine. Season with salt, then spoon sauce and beans around chicken. Discard whole chiles if desired.
