In a large skillet, cook onion and garlic in hot oil over medium heat about 4 minutes or until tender. Stir in shredded chicken, mustard, apricot preserves, vinegar, bourbon, and cayenne pepper. Heat through. If necessary, simmer, uncovered, about 5 minutes or until desired consistency.
Spoon about ½ cup chicken mixture on each bun bottom. Top with red onion if desired. Add bun tops.