Prep the chicken and broccoli. Slice the chicken into thin strips for quick, even cooking. Cut broccoli into bite-size florets.
Pat chicken dry and season lightly with salt and pepper.
Stir together the sauce. In a bowl, whisk broth, soy sauce, oyster or hoisin (if using), vinegar, honey, sesame oil, and sriracha. In a separate small cup, mix cornstarch with 2 tablespoons water until smooth. Stir the slurry into the sauce.
Set aside.
Heat the pan. Set a large skillet or sauté pan over medium-high heat. Add 1–2 tablespoons oil and let it shimmer.
Brown the chicken in batches. Add half the chicken in a single layer. Cook 2–3 minutes per side until lightly browned and mostly cooked through.
Transfer to a plate and repeat with the remaining chicken, adding more oil if needed. Don’t crowd the pan—browning adds flavor.
Cook the aromatics. Reduce heat to medium. Add a drizzle of oil if the pan is dry, then add onion. Sauté 2 minutes until softened.
Stir in garlic and ginger for 30–45 seconds until fragrant.
Steam-sauté the broccoli. Add the broccoli and 2 tablespoons water. Cover the pan (use a lid or sheet pan) and steam 2–3 minutes until bright green and just tender. Remove the lid and let any excess moisture cook off.
Combine chicken and sauce. Return the chicken and any juices to the pan.
Whisk the sauce again (cornstarch settles), then pour it in. Stir and cook 1–3 minutes until the sauce thickens and coats everything. If it gets too thick, add a splash of water or broth.
Taste and finish. Adjust with more soy for salt, vinegar for brightness, or honey for sweetness.
Sprinkle sesame seeds and green onions if you like. Serve hot over rice, noodles, or as is.