Whisk the broth, 3 cups water, tomato paste, brown sugar, molasses, mustard, barbecue seasoning and garlic in a slow cooker. Add the beans. Push a clove into each onion half; tuck the onions and sausages into the beans in the slow cooker. Cover and cook on high until the beans are tender, about 6 hours.
Discard the onion halves. Stir in the vinegar and Worcestershire sauce, then let the mixture sit, uncovered, about 15 minutes. (The longer the beans sit, the more flavorful they will be.) Garnish with pickled peppers, scallions and/or sour cream, if desired.