Pour olive oil into a medium saucepan over medium-high heat. Add onion and garlic and cook, stirring often, until limp, 3 to 4 minutes. Add Zinfandel, ketchup, cherries, vinegar, Worcestershire, brown sugar, mustard, ginger, black pepper, anise seeds, and cayenne. Bring to a boil, then reduce heat and simmer, stirring occasionally, until liquid begins to thicken slightly, about 20 minutes. Let cool slightly.
Pour mixture into a blender and add 2 tbsp. lemon juice; whirl until very smooth. Taste and add more lemon juice if desired. Use warm or at room temperature.
Note: Nutritional analysis is per 1/4 cup.