In a medium saucepan, heat a drizzle of oil over medium-high heat and cook the onion for 3-4 minutes, until soft; add the garlic and cook for another minute or two.
Add the remaining ingredients and bring to a simmer; cook for 10-15 minutes, until the mixture thickens.
Purée with a hand-held immersion blender or cool and purée in a blender or food processor until smooth.
Use as you would any barbecue sauce—on grilled meats, in baked beans or drizzled on burgers. Makes about 3 cups.