Whisk together all the sauce ingredients in a small bowl and set aside.
Toss the chicken with 1 tablespoon cornstarch.
Heat 1 tablespoon oil in a large skillet or wok over medium-high heat. Add the chicken in a single layer and cook 5–6 minutes, stirring occasionally, until golden and cooked through. Transfer to a plate.
Add the remaining oil, then the bell pepper, broccoli, and snap peas. Stir-fry 3–4 minutes, until crisp-tender.
Return the chicken to the pan. Stir the sauce, pour it in, and toss for 1–2 minutes until thick and glossy.
Top with green onions and sesame seeds and serve over rice or noodles.