In a medium bowl, toss the thin chicken slices with the cornstarch, soy sauce, and sesame oil until every piece is lightly coated. Set aside for 10 minutes while you prep the vegetables — this quick velveting step is what keeps stir-fried chicken breast silky instead of dry.
In a small bowl or measuring cup, whisk together the soy sauce, oyster sauce, honey, garlic, ginger, sesame oil, black pepper, and red pepper flakes (if using). Stir the cornstarch slurry separately and keep it nearby — it goes in at the very end to gloss up the sauce.
Heat 1 tablespoon of high-smoke-point oil (avocado or peanut) in a large wok or skillet over the highest heat until it just starts to smoke. Add the chicken in a single layer and sear undisturbed for 1–2 minutes, then toss and cook 2–3 minutes more until golden at the edges and cooked through (165°F / 74°C internal temperature). Transfer to a clean plate.
Add another teaspoon of oil to the screaming-hot wok. Add the carrots and broccoli first and stir-fry 2 minutes, then add the bell peppers and snap peas and cook 2–3 minutes more, tossing constantly, until the vegetables are bright and crisp-tender. Add the green onions in the last 30 seconds.
Return the chicken to the wok. Give the sauce a quick re-whisk, pour it over everything, and toss to coat. Drizzle in the cornstarch slurry while tossing; cook 1 minute until the sauce turns glossy and clings to the chicken and vegetables. Serve immediately over hot jasmine rice.