Preheat broiler. In a small bowl, use a fork to whisk together hoisin sauce, garlic and ginger.
Brush both sides of chicken with hoisin mixture. Spray broiler pan with cooking spray then place chicken on broiler pan and broil for 6 minutes on each side or until done and no longer pink in the middle.
Heat vegetable oil in a skillet over medium-high heat. Sauté onion for 2 minutes then add red and green cabbage and saute for 2 minutes or until cabbage starts to wilt.
Place cabbage in a medium bowl and add sesame oil, salt and pepper then toss to coat.
