Chicken Marinade: In a large mixing bowl, stir together soy sauce (1 tablespoon), rice wine or sherry (1 tablespoon), and cornstarch (2 teaspoons) until cornstarch is dissolved. Add sliced chicken and toss to coat. Let stand at room temperature for 10-15 minutes.
Meanwhile, Make The Sauce: Whisk together the sauce ingredients in a small bowl until the brown sugar and cornstarch are dissolved; set aside
Stir Fry: Heat 1-2 tablespoons oil in a 12-inch, nonstick skillet, over high heat. Add the half chicken, spreading it out in a single layer, and brown, for about 30 seconds, on each side. Remove to a plate. Repeat with the remaining chicken, adding more oil to the skillet as needed.
Drain all but 1 tablespoon oil from the pan. Add the ginger (2 teaspoons) and garlic (4 cloves) and cook until fragrant, about 30 seconds. Add the carrots (1 cup) and cook, stirring frequently, until they begin to soften for about 1 minute. Add 1 cup of green onion and cook for another 30 seconds. Add the sauce and bring to a boil. Cook until the sauce thickens, about 1 minute. Add chicken back to the skillet and continue to cook until heated through. Garnish with the remaining 1/2 cup green onions and sesame seeds. Serve over cooked white rice.