1. Heat oil in a 4-qt. pot over medium heat. Add onion and garlic and cook until translucent, about 15 minutes.
2. Add sugar and peppercorns and cook, stirring frequently until sugar melts, about 1 minute. Add ketchup, liquid smoke, and Coke reduction. Reduce heat to a simmer.
3. Cook for 1 hour to meld flavors. Using a blender, whirl mixture until smooth, about 4 minutes.