Heat the olive oil in a saucepan over medium-high heat. Stir in the onion, garlic, and ginger, and cook until tender. Reduce heat to low.
Mix in ketchup, SPLENDA® Brown Sugar Blend, molasses, rum, hoisin sauce, tomato paste, vinegar, chili powder, and cayenne pepper. Cook and stir 5 minutes, until well blended and heated through. Stir in remaining rum.