Melt butter in medium saucepan over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic and cook until fragrant, about 30 seconds.
Add tomato sauce, cider vinegar, rice vinegar, molasses, Worcestershire sauce, brown sugar, mustard, hot sauce, salt, black pepper, and cayenne and stir to combine. Bring to a boil, then reduce heat to low and simmer until slightly thickened, about 15-20 minutes, stirring occasionally.
Transfer sauce to a blender and blend until smooth. Let cool to room temperature, transfer to a jar and store in refrigerator for up to a month.