In a large mixing bowl, combine the cornstarch and chicken. Toss to coat the chicken in cornstarch.
In a medium mixing bowl, whisk together the soy sauce, ¼ cup water, brown sugar, toasted sesame oil, and ginger. In a small mixing bowl, whisk together the cornstarch and 1 tablespoon of water and then whisk the cornstarch mixture into the rest of the sauce. Set aside.
In a large, heavy-bottomed skillet or wok, heat 2 tablespoons of vegetable oil over medium-high heat. Add the chicken and saute until browned on all sides. Remove the chicken from the pan and set aside.
Add the remaining vegetable oil to the skillet and let it heat up for a few seconds. Add the white parts of the green onion and saute for 1 minute. Add the garlic and saute for 30 seconds.
Return the chicken to the pan and pour the sauce over it. Cook, stirring occasionally, until the sauce thickens and the chicken is cooked through.
Serve warm garnished with the green parts of the green onions.