Cut the chicken breasts into bite-sized pieces.

In a bowl, combine the soy sauce, honey or brown sugar, rice vinegar, sesame oil, garlic, and ginger. Add the chicken pieces to the bowl and let them marinate for at least 15 minutes.

Cook the rice according to the package instructions. This usually takes about 15-20 minutes.

Heat 1 tablespoon of olive oil in a large pan over medium heat. Add the marinated chicken pieces and cook until they are fully cooked and slightly browned, about 5-7 minutes.

In a small bowl, mix the cornstarch and water until smooth. Add this mixture to the pan with the chicken and cook for another 2-3 minutes until the sauce thickens.

In another pan, heat 1 tablespoon of olive oil over medium heat. Add the broccoli florets, bell pepper slices, and shredded carrots. Sauté for about 5-7 minutes until the vegetables are tender but still crisp.

Divide the cooked rice into bowls. Top with the cooked chicken and sautéed vegetables. Sprinkle with sesame seeds if desired.