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Melt butter with olive oil in a large saute pan over low heat. Add potatoes, stirring to coat, and cook, stirring, until golden brown, 10 to 15 minutes.
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Add onion, garlic, ginger, mustard seeds, curry paste, chile powder, and cardamom. Stir well and cook until onions are tender, about 20 minutes.
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Add plantains, and cook until softened, about 10 minutes. Let cool. Season with salt; stir in scallions just before serving. Plantain chutney may be kept in an airtight container, refrigerated up to 3 days.