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Heat 1 tablespoon butter in a 10-inch heavy skillet over moderately high heat until foam subsides, then sauté half of bananas, cut sides down first, turning over once, until golden, 1 1/2 to 2 minutes total. Transfer with a slotted spatula to 2 dessert bowls. Heat 1 tablespoon butter and sauté remaining bananas in same manner, transferring to 2 more bowls.
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Melt remaining 2 tablespoons butter in skillet over moderate heat, then add brown sugar, cream, cardamom, and a pinch of salt and simmer, stirring occasionally, until sauce is slightly thickened, about 2 minutes. Remove from heat and stir in lime juice.
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Spoon sauce over bananas and ice cream
