Marinate the chicken by whisking together soy sauce, brown sugar, honey, rice vinegar, sesame oil, minced garlic, and grated ginger. Coat the chicken and refrigerate for at least 30 minutes.
Grill the marinated chicken for 6-7 minutes on each side until the internal temperature reaches 165°F. Let it rest before slicing.
Steam the broccoli in a pot over boiling water for 5-7 minutes until tender and bright green.
Thicken the reserved marinade by boiling it and adding a cornstarch-water mixture. Stir until thickened.
Serve the sliced chicken over cooked white rice, drizzle with teriyaki sauce, and arrange steamed broccoli on the side. Garnish with sesame seeds if desired.