If using wooden skewers, soak them in water for 30 minutes to prevent burning on the grill.
In a bowl, whisk together soy sauce, honey (or sugar), rice vinegar, sesame oil, garlic, and ginger.
Place the cubed chicken in a resealable bag or bowl. Pour in about ¾ of the marinade, reserving the rest for later. Marinate in the fridge for at least 30 minutes or up to 4 hours.
While the chicken marinates, pour the reserved marinade into a small saucepan. Bring to a simmer. If desired, add the cornstarch slurry and cook until thickened, about 2–3 minutes. Set aside.
Thread the marinated chicken pieces onto skewers, leaving a little space between each piece for even cooking.
Preheat grill or broiler to medium-high. Grill skewers for 5–7 minutes per side or until cooked through and lightly charred. Baste with the teriyaki glaze during the last few minutes of cooking.
Remove skewers from the grill and brush with additional glaze. Sprinkle with sesame seeds and green onions if desired. Serve over steamed rice, noodles, or with grilled vegetables.