Add onions; cover. Cook 9 min. or until onions are tender, uncovering after 3 min. and stirring frequently. Stir in garlic; cook 8 to 10 min. or until onions are golden brown, stirring occasionally. Stir in 3 Tbsp. steak sauce and sugar; cook and stir 2 min.
Place chicken in shallow baking dish.
Mix remaining steak sauce and mustard; spread over chicken. Top with onions.
Bake 30 min. or until chicken is done (165F).
Serve topped with cheese and sauce from bottom of dish.