Heat the oil in a small saucepan over medium heat. Add the onion and cook, stirring until softened, about 5 minutes. Stir in the ginger, turmeric, allspice, garlic and jalapeno and cook, stirring until fragrant, about 1 minute. Add the tomato paste and cook, stirring until lightly caramelized, about 1 minute. Add the mashed bananas, vinegar, brown sugar, soy sauce and rum, if using, and simmer, stirring occasionally, until slightly thickened, about 10 minutes. Scrape the sauce into a bowl, press a sheet of plastic wrap on the top and let cool. Refrigerate in an airtight container for up to 2 weeks.
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