Prep the chicken: Thinly slice the chicken breast against the grain. In a bowl, toss with 1 tablespoon soy sauce and 1 tablespoon cornstarch.
Set aside while you prep the vegetables.
Make the sauce: In a measuring cup, whisk the broth, soy sauce, oyster sauce, hoisin, rice vinegar, sriracha, sesame oil, cornstarch, and honey. Stir until smooth and no cornstarch lumps remain.
Heat the pan: Place a large skillet or wok over medium-high heat. Add 1 tablespoon oil.
When it shimmers, add the chicken in a single layer. Cook 3–4 minutes, stirring once or twice, until just cooked through and lightly browned. Transfer to a plate.
Stir-fry the veggies: Add the remaining 1 tablespoon oil to the pan.
Add broccoli and carrots first; cook 2 minutes, stirring often. Add bell pepper, onion, and snap peas; cook another 2–3 minutes until crisp-tender.
Add aromatics: Push veggies to the edges. Add garlic and ginger to the center.
Stir 30 seconds until fragrant, then toss everything together.
Sauce it up: Return chicken and any juices to the pan. Give the sauce a quick stir (cornstarch settles), then pour it in. Stir constantly for 1–2 minutes until the sauce thickens and coats everything.
Taste and finish: Adjust seasoning with a splash more soy sauce for salt, vinegar for brightness, or sriracha for heat.
Remove from heat.
Serve: Spoon over rice or cauliflower rice. Top with green onions, sesame seeds, and a squeeze of lime if you like.