Prep the chicken: Pat the chicken dry and slice into thin strips.
Toss with 2 tablespoons cornstarch and a pinch of salt until lightly coated. Set aside while you prep the vegetables.
Make the sauce: In a small bowl, whisk soy sauce, rice vinegar, honey, lime juice, chicken broth, 1 tablespoon cornstarch, and sriracha. Stir until smooth and no lumps remain.
Taste and adjust sweetness, salt, or heat.
Heat the pan: Set a large skillet or wok over medium-high heat. Add 1 tablespoon neutral oil and swirl to coat until shimmering.
Sear the chicken: Add half the chicken in a single layer. Cook 2–3 minutes per side until browned and just cooked through.
Remove to a plate. Repeat with remaining chicken, adding more oil if needed.
Cook the vegetables: Add the remaining neutral oil to the pan. Toss in the onion, bell pepper, and carrot.
Stir-fry 2 minutes until slightly tender but still crisp. Add broccoli and snap peas; cook 2–3 minutes more.
Add aromatics: Push vegetables to the edges. Add toasted sesame oil to the center, then stir in ginger and garlic.
Cook 30 seconds until fragrant; avoid browning.
Combine: Return chicken and any juices to the pan. Stir the sauce again and pour it in. Toss everything together and cook 1–2 minutes until the sauce thickens and coats the chicken and vegetables.
Finish: Sprinkle in sesame seeds.
Turn off the heat. Taste and adjust with extra soy, lime, or honey as needed.
Serve: Spoon over warm rice or noodles. Garnish with cilantro, extra sesame seeds, and lime wedges.