In a large bowl, combine soy sauce, brown sugar, honey, rice vinegar, sesame oil, garlic, and ginger. Whisk until the sugar is dissolved.
Add the chicken thighs to the marinade, ensuring they are well coated. Cover and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
Preheat your grill or a large skillet over medium-high heat. Remove the chicken from the marinade, reserving the marinade for later.
Grill or cook the chicken for about 5-7 minutes on each side, or until fully cooked and the internal temperature reaches 165°F. Remove from heat and let rest for 5 minutes.
While the chicken is resting, pour the reserved marinade into a small saucepan. Bring to a boil over medium heat. In a small bowl, mix cornstarch and water until smooth, then add to the saucepan. Stir until the sauce thickens, about 2-3 minutes.
Steam the broccoli florets until tender, about 5 minutes.
Slice the chicken and serve it over steamed broccoli, drizzled with the thickened teriyaki sauce. Garnish with sesame seeds and sliced green onions if desired.