If you are going asian (an assumption on carmelized and pickled onions) you might want to try a rice vinegar, mirin and dried red chile sauce reduction. Like the viinegar sauce used in carolina boston butt recipes. Otherwise I would use one of the traditional BBQ sauces on this site (provided by some of the best BBQ people on the web) and cut it with a rich au jus to make a really nice dipping sauce. BOLHTH.
I would turn it into a banh mi style sandwich. Use a mix of mayo sriacha/sambal and top it with pickled julienne carrots and daikon radish. Then top that with fresh cilantro, green onion, and paper thin slices of red jalepeno.