Preheat oven to 400 °F. Line a 13- x 9-inch baking dish with heavy duty aluminum foil and coat the foil with nonstick cooking spray.
In a medium saucepan, whisk together the soy sauce, mirin, sugar, sesame oil, ginger, and parlic. Place over MEDIUM-HIGH heat. In a meauring cup or a small bowl, whisk the water and cornstarch until dissolved and then add the mixture to the pan. Bring just to the boiling point then reduce heat to MEDIUM-LOW and cook for several minutes, stirring, until thickened. Remove from the heat.
Place the chicken in the prepared pan and season on both sides, to taste, with salt and freshly ground black pepper. Spoon about one-third (about ¾ cup) of the teriyaki sauce over the chicken, being sure to coat each piece. Reserve the remaining sauce.
Cover the dish with foil and bake for 30 minutes. Remove the foil and carefully spoon off or drain the thin cooking liquid that has collected in the bottom of the pan. Spoon the reserved thickened sauce evenly over the chicken. Return the dish to the oven and bake, uncovered, for 15 to 20 minutes, or until the chicken reaches an internal temperature of 175 °F for thighs or 165 °F for breasts. Remove from the oven and let the chicken rest for 5 minutes. The sauce will continue to thicken as it rests. Spoon some of the sauce over the chicken and garnish with sesame seeds and sliced green onions before serving.
Serve with rice and vegetables with additional teriyaki sauce spooned over the chicken and rice, if desired.