In a large bowl, whisk together the egg, 2 tablespoons of cornstarch, and a pinch of salt and pepper. Trim any excess fat from the chicken, then cut them into 1-inch pieces and toss with the egg mixture.

Optional: Cut up the veggies, heat a skillet (medium-high) with a couple tablespoons of oil, and toss the veggies in with some salt and pepper. Stir fry the vegetables for several minutes, stirring occasionally, until they soften slightly (but retain their crunch). Set aside.

At the same time you start the vegetables, heat a large skillet with the vegetable oil over medium-high heat for the chicken.

When the oil is very hot (it'll look wavy on the surface), add the chicken and all of the egg mixture. Cook, stirring occasionally, until it is golden brown and cooked through. This will take about 7-10 minutes. 

While the chicken is cooking, prepare the sauce. In a small bowl whisk the soy sauce, water, sesame oil, brown sugar, rice vinegar, fresh ginger, minced garlic, cornstarch, and sesame seeds together.

Once the chicken is cooked through and golden brown, pour the sauce over top. Toss the chicken to coat in the sauce, which will begin to thicken as soon as it hits the hot skillet.

Once the chicken is coated and the sauce thickened, turn off the heat. Serve over a bed of rice and sprinkle the sliced green onions over top.