In a large bowl, add hot peppers, garlic, basil, brown sugar, honey and rum. Mix well.
Spread the mixture over a baking sheet, reserving any remaining liquid from the bowl.
Roast in the oven for 12 minutes at 350 degrees F.
Cool, then add the mixture to a food processor with the reserved liquid, apple cider vinegar and salt to taste. Process until smooth.
With a fine mesh strainer, pour the liquid into a bowl. Get all the liquid out until you are left with a paste. Toss the paste.
Swirl in lime juice and pour the sauce into a glass container or bottle. Cover and let it sit for at least 24 hours or longer for the flavors to blend.