In a medium bowl, whisk together soy sauce, honey, rice vinegar, minced garlic, and minced ginger. Set aside.
In a large skillet, heat vegetable oil over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes.
Add the broccoli, red bell pepper, and carrot to the skillet. Stir-fry for an additional 3-4 minutes until the vegetables are tender-crisp.
In a small bowl, mix cornstarch and water until smooth. Add this mixture to the skillet along with the soy sauce mixture. Stir well to coat the chicken and vegetables. Cook for another 2-3 minutes until the sauce thickens.
Serve the teriyaki chicken and vegetables over a bed of cooked rice. Garnish with sesame seeds and sliced green onions.