In a large saucepan, heat the olive oil over medium heat and add the onion and garlic. Cook for 3-4 minutes or until softened and slightly translucent. Add the jalapenos and ginger and cook until fragrant, about 2 minutes.
Add the pineapple, brown sugar, dry mustard, cayenne pepper, salt, pepper, pineapple juice, golden rum, ketchup, apple cider vinegar, worcestershire sauce and molasses. Stir to combine.
Heat the sauce to boiling, then reduce heat to a rapid simmer and cook, uncovered for 15-20 minutes or until the mixture has reduced and thickened.
Transfer to a blender or food processor and pulse until the sauce is smooth. Use on chicken, pork and shrimp or other seafood.