In a medium saucepan, whisk together the soy sauce, brown sugar, mirin, sesame oil, minced garlic, and grated ginger. Bring the mixture to a simmer over medium heat, whisking until the sugar has completely dissolved.

Place your cubed chicken in a large bowl or a resealable plastic bag. Pour about half of the warm teriyaki marinade over the chicken. Reserve the other half of the sauce in the saucepan for later; this will become our glaze. Toss the chicken to ensure it’s fully coated. Cover the bowl or seal the bag and let it marinate in the refrigerator for at least 30 minutes.

While the chicken is marinating, let’s finish our glaze. In a small bowl, whisk together the cornstarch and cold water to create a slurry. Slowly pour the slurry into the saucepan with the reserved marinade, whisking constantly. Continue to simmer the sauce over medium low heat for 3 to 5 minutes, or until it has thickened enough to coat the back of a spoon.

If you haven't already, toss your chopped bell peppers and onion with olive oil, salt, and pepper. Thread the marinated chicken pieces and vegetables onto your skewers, alternating between them. Leave a little space to ensure even cooking.

Preheat your grill to medium high heat. Place the skewers on the grill and cook for about 10 to 15 minutes, turning occasionally, until the chicken is cooked through and has beautiful char marks. Baste the skewers with the reserved thickened teriyaki glaze during the last few minutes of cooking.

Transfer the skewers to a platter. Garnish generously with toasted sesame seeds and freshly sliced scallions. Serve them hot with your favorite sides.