For marinade: Combine all ingredients in a medium bowl and add chicken pieces. Toss to coat and marinate for 30 minutes.
For sauce: Place all ingredients in a small saucepan and heat on low, stirring until sugar has dissolved. Remove from heat and set aside.
For chicken: Place a wok or large heavy skillet over high heat and add about 3 Tablespoons oil. When hot, add chicken, tossing and cooking until chicken begins to brown. Remove to a plate. Add remaining oil to wok and when hot, add garlic and ginger. Cook for about 1 minute. Add vegetables; tossing and cooking for about 2 more minutes. Return chicken to the pan and cook for another minute. Add sauce and stir to coat. Add a dash of sesame oil and scallions and serve immediately.