Toss sliced chicken with cornstarch, soy sauce, and Shaoxing wine. Rest 15 minutes.
Combine sauce ingredients in a small bowl and set aside.
Heat skillet on high 3 to 4 minutes. Add 2 tablespoons oil. Add chicken in single layer. Sear 60 seconds, then stir-fry 90 seconds. Remove.
Add remaining oil. Stir-fry bell pepper and broccoli 90 seconds. Add garlic, ginger, white parts of green onions. Stir 20 seconds.
Return chicken to pan. Pour sauce around edges. Toss 60 to 90 seconds until thickened. Top with green onion tops.