Whisk soy sauce, honey, rice wine vinegar, cornstarch, garlic, sesame oil, and ginger in a small bowl until the cornstarch fully dissolves. Set aside.
Pat chicken dry and season generously with salt and black pepper.
Heat oil in a large skillet over medium-high heat. Add chicken and cook 6–7 minutes, stirring occasionally, until cooked through and lightly golden.
Add broccoli florets and sliced bell pepper to the skillet. Stir-fry 3–4 minutes until vegetables are tender-crisp.
Pour in the teriyaki sauce, stirring constantly. Cook 1–2 minutes until the sauce thickens and coats the chicken and vegetables.
Remove from heat and let cool on the counter for at least 20 minutes before sealing any containers.
Divide cooked brown rice among 4 containers. Top with the chicken and vegetable mixture, garnish with sesame seeds if using, label with the date, and refrigerate.