Combine sauce ingredients. Add half of the sauce to a zippered gallon bag along with chicken. Let marinate for at least 4 hours (up to overnight). Cover the remaining sauce and keep in refrigerator until ready to prepare the rest of the meal.
In a pot over medium heat, add rice, water, vinegar, salt, ginger and garlic. Cover and cook for 20 minutes. Remove from heat but do not remove the lid.
Remove chicken from zippered bag. Pour remaining sauce into a small saucepan over medium-low heat. Add the additional sauce from earlier. Allow to simmer while preparing the rest of the meal.
Add chicken breast to a grill pan over medium high heat. Cook for 7 minutes then baste with sauce and flip. Baste again with sauce and let cook for another 7 minutes. Check with meat thermometer and remove from heat once it has reached 165degF.
Add the broccoli, carrots and white onions to the same pan, along with half a cup of sauce. Saute until fork tender.
Add a portion of rice to the bottom of a shallow bowl. Then add a portion of the mixed veggies. Slice each chicken breast into strips and add to rice. Spoon more KBBQ sauce over the top and then sprinkle with sesame seeds.