Reduce the Dr Pepper: Pour the Dr Pepper into a medium saucepan and bring to a boil over medium-high heat. Simmer, stirring occasionally, until reduced to a syrup, about ½ cup (8–10 minutes). Watch closely at the end so it doesn't scorch.
Build the base: Reduce heat to medium-low. Whisk in the tomato puree, tomato paste, vinegar, brown sugar, molasses, and Worcestershire sauce until smooth.
Season: Whisk in the black pepper, smoked paprika, garlic powder, onion powder, chili powder, salt, cayenne, and liquid smoke (if using) until fully combined.
Simmer: Bring to a gentle simmer, then reduce heat to low. Cook uncovered for 20–25 minutes, stirring often, until thick and glossy.
Cool and store: Remove from heat and let cool (it thickens as it sits). Taste and adjust seasoning, then transfer to a clean jar.