Sweet floral bananas stand in for tomatoes in this spicy condiment that is unique to the Philippines, where a tomato shortage and concurrent banana surplus during World War II led to the invention of ketchup made with the tropical fruit. Use the ketchup like you would a chutney: as a dip for vegetables, as a spread on sandwiches, or as a sauce for grilled or roast chicken or pork.
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Refrigerate in an airtight container for up to 2 weeks.
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.