In a medium bowl, whisk together the soy sauce, brown sugar, honey, minced garlic, and minced ginger until well combined.

Place the chicken thighs in a large resealable plastic bag or a shallow dish. Pour the marinade over the chicken, seal the bag or cover the dish, and refrigerate for at least 30 minutes, or up to 4 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 6-7 minutes on each side, or until the internal temperature reaches 165°F. Remove the chicken from the heat and let it rest for a few minutes before slicing.

While the chicken is resting, pour the reserved marinade into a small saucepan. In a separate small bowl, mix the cornstarch and water to create a slurry. Add the slurry to the saucepan and bring the marinade to a boil over medium heat, stirring constantly until it thickens.

Steam the broccoli florets until tender, about 4-5 minutes.

Serve the sliced teriyaki chicken over cooked rice, drizzled with the thickened sauce, and alongside the steamed broccoli. Sprinkle with sesame seeds if desired.