How to Make It
Heat the oil in a large saucepan. Add the garlic, onion, green pepper and a large pinch of salt and cook over moderate heat, stirring occasionally, until softened, about 10 minutes. Add the rum and simmer for 2 minutes. Add the chili powder, black pepper, allspice and cloves and cook, stirring, until fragrant, about 3 minutes. Add the brown sugar, water, ketchup, molasses, mustard, vinegar and hot sauce and simmer over moderate heat, stirring often, until thickened, about 30 minutes.
Transfer the barbecue sauce to a large food processor and puree. Season the sauce with salt.