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Preheat oven to 375 degrees F.
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Bake potatoes until very soft, about 1 hour; let cool slightly.
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Once potatoes are cool enough to handle, peel and mash.
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In a small saucepan, over low heat, combine coconut milk and curry paste.
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Combine, coconut mixture, half the sugar, half the butter, and the salt with the potatoes; keep warm (or cover and refrigerate for up to 2 days).
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About 30 minutes before serving, place potatoes in a baking dish, cover with foil, and bake for 20 minutes.
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Uncover potatoes, dot with remaining butter, sprinkle remaining sugar over top, and broil until browned and crusty (do not burn).