Melt butter in a saucepan over medium heat and add onion. Soften for 5 minutes. Add rum and spices and cook an additional 5 minutes.
Add all other ingredients and whisk together until combined. Bring to a boil, then lower heat to a simmer. Simmer for 10 minutes, stirring occasionally so it doesn't burn.
Use a slotted spoon to remove onions, or use an immersion blender to puree them into the sauce. Allow to cool and serve.
Notes
*Make sure your Worcestershire sauce and liquid smoke say "gluten free" on the bottle. You can find them GF and non-GF.Click on the time in the directions to start a timer!