It's worth it to make a big batch of barbecue sauce. Freeze it in small or large containers to give quick flavor to chicken anytime.
In a medium saucepan, heat oil over medium. Add onion and cook until completely soft, about 5 minutes. Add garlic and cook until fragrant, 1 minute.
Add tomato paste and mustard; cook, stirring constantly, until paste turns a brick-red color, about 5 minutes. Add 2 cups water, tomato sauce, molasses, Worcestershire, vinegar, salt, and pepper and stir until smooth.
Bring to a simmer; reduce heat to low and partially cover. Simmer, stirring occasionally, for 2 hours (thin with water if sauce becomes too thick). Season to taste with vinegar, salt, and pepper. Let cool completely before using.