Heat oil in a sauce pan, add onions and cook until translucent.
Add garlic, jalapenos, ginger, turmeric, and allspice; stirring until fragrant.
Stir in bananas, vinegar, honey, rum, tomato paste, soy sauce and salt.
Bring to a boil, lower heat to a simmer.
Cover and cook for 15 minutes, stirring often.
Remove from heat and let cool for 10 minutes.
Puree until smooth, adding water for consistency.