Make the sauce: Combine cornstarch and water in a small bowl. In a medium saucepan, add the remaining ingredients along with the cornstarch/water mixture. Stir frequently, and bring the sauce to a simmer. Cook until the sauce lightly thickens, it will be dark brown. Once the sauce has thickened up, remove it from the heat and let cool completely. (you can place it in the fridge to speed up the process)
Once the sauce is completely cooled, place the cubed chicken in a large ziplock bag. Pour half of the sauce over the chicken and gently shake to coat the chicken. Let chicken marinate in the fridge for at least 30 minutes. Place remaining sauce aside for later.
When the chicken is done marinating, place your chicken on skewers and heat the grill pan or grill to medium heat.
Once the grill is hot, place skewers on a lightly oiled grill pan or grill. Turn the skewers every 3-4 minutes until the chicken is cooked through (internal temp 165 degrees), about 20-30 minutes. During the last few turns baste with the remaining teriyaki sauce.
Remove skewers from the grill and serve with chopped green onions and a sprinkle of sesame seeds (optional).