Prep the chicken and broccoli. Slice the chicken into thin strips. Cut broccoli into bite-size florets. Pat the chicken dry with paper towels to help it brown well.
Toss the chicken with cornstarch. In a bowl, combine the chicken with 1 tablespoon cornstarch, a pinch of salt, and a little pepper.
This helps the chicken sear and gives the sauce something to cling to.
Make the sauce. In a small bowl, whisk together sweet chili sauce, soy sauce, rice vinegar, garlic, ginger, water or broth, and 2 teaspoons cornstarch. If you like it spicier, add a pinch of red pepper flakes.
Sear the chicken. Heat 1–2 tablespoons oil in a large skillet or wok over medium-high heat. Spread the chicken out in a single layer.
Cook for 4–6 minutes, turning once, until browned and just cooked through. Remove to a plate.
Cook the broccoli. Add another splash of oil if the pan looks dry. Toss in the broccoli and a big pinch of salt.
Stir-fry for 3–4 minutes until bright green and crisp-tender. If you prefer softer broccoli, add 2 tablespoons water and cover for 1–2 minutes to steam.
Combine and sauce. Return the chicken to the pan. Give the sauce a quick stir and pour it in.
Reduce heat to medium and toss everything until the sauce thickens and coats the chicken and broccoli, 1–2 minutes.
Finish and serve. Drizzle with sesame oil if using. Top with green onions and sesame seeds. Serve hot over steamed rice or noodles.