In a large bowl, add 1 cup teriyaki sauce, ginger (optional), and garlic (optional), and mix well. Add remaining ingredients and mix well.
Heat grill and grill basket.
Hold as much of the sauce back as possible and tumble the chicken and vegetables onto the grill basket and evenly distribute the vegetables. Allow to cook for 5 minutes without turning. Use a metal spatula and turn vegetables. Pour remaining vegetable marinade over and allow to cook for 4 minutes and turn. Cook until the chicken is cooked through and the vegetables have browned about 10-12 minutes total. Remove to a clean bowl
Heat 1 cup of teriyaki marinade in microwave for 1 minute. Pour over chicken and toss. Sprinkle with sesame seeds and toss.
Serve over rice.
7 WW points without the rice.