Heat oil in a large saucepan over medium heat. Add onion and cook, stirring occasionally, until tender and just starting to brown, 2 to 4 minutes. Add garlic and jalapeno and cook, stirring, until fragrant, about 30 seconds. Add bourbon, increase heat to high and bring to a boil; cook until most of the liquid has evaporated, about 5 minutes. Stir in blueberries, ketchup, vinegar, brown sugar, molasses and allspice; return to a boil. Reduce the heat and simmer, stirring occasionally, until thickened, about 20 minutes.