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

Reserve 1/4 cup of the marinade for basting later. Pour the remaining marinade over the chicken breasts in a large resealable plastic bag or shallow dish. Seal or cover and marinate in the refrigerator for at least 1 hour, or up to overnight for maximum flavor.

Preheat your grill to medium-high heat. While the grill is heating, prepare the teriyaki sauce by pouring the reserved marinade into a small saucepan. In a separate bowl, mix the cornstarch and water until smooth, then add it to the saucepan.

Bring the sauce to a gentle boil over medium heat, stirring constantly until it thickens, about 3-5 minutes. Remove from heat and set aside.

Remove the chicken from the marinade and discard the used marinade. Grill the chicken for 6-7 minutes on one side, then flip and brush with the prepared teriyaki sauce. Grill for an additional 5-7 minutes, or until the chicken reaches an internal temperature of 165°F (75°C).

Once cooked, remove the chicken from the grill and let it rest for 5 minutes before slicing. Drizzle additional teriyaki sauce over the chicken and garnish with sesame seeds and chopped green onions, if desired. Serve with rice and vegetables.