Place the mangos, bananas, sweet onions, tomato paste, garlic, salt, brown sugar, molasses, balsamic vinegar, and Worcestershire sauce in a food processor and pulse until pureed.
Transfer puree to a saucepan. Add ground chipotle pepper, ginger, cinnamon, allspice, nutmeg, cloves, and water. Stir to combine. Bring to a low boil. Reduce heat and simmer, stirring often, for 15 minutes. Let cool to room temperature to serve. Cover and refrigerate leftovers and use within two weeks.