Prep everything first. Stir-fries move fast, so slice the chicken and veggies, mince the garlic and ginger, and separate the lettuce leaves. Pat the lettuce dry so it stays crisp.
Toss chicken with cornstarch. In a bowl, combine the sliced chicken with 1 tablespoon cornstarch and a pinch of salt.
This helps the chicken brown and stay tender.
Whisk the sauce. In a small bowl, whisk soy sauce, oyster sauce (if using), rice vinegar, honey, sesame oil, broth, 1 teaspoon cornstarch, and optional chili. Set aside.
Heat the pan. Warm a large skillet or wok over medium-high heat. Add the oil and swirl to coat.
Cook the chicken. Add chicken in an even layer.
Let it sear for 1–2 minutes before stirring. Cook until just no longer pink, about 4–5 minutes. Remove to a plate.
Stir-fry the veggies. Add a touch more oil if needed.
Add broccoli, carrots, and bell pepper first; cook 2 minutes, stirring often. Add zucchini, snap peas, and the white parts of green onions; cook 2–3 minutes more until crisp-tender.
Add aromatics. Push veggies to the sides. In the center, add garlic and ginger.
Stir 30 seconds until fragrant.
Combine and sauce. Return chicken and any juices to the pan. Pour in the sauce and toss. Cook 1–2 minutes until the sauce thickens and glazes everything.
Remove from heat and sprinkle with the green parts of the green onions.
Assemble cups. Spoon the stir-fry into lettuce leaves. Top with sesame seeds and a squeeze of lime. Serve immediately.