Make the sauce. In a bowl, whisk soy sauce, honey, rice vinegar, mirin, water, cornstarch, sesame oil, garlic, ginger, and red pepper flakes until smooth.
Set aside.
Prep the chicken and veggies. Pat the chicken dry and cut it into bite-size pieces. Slice the bell pepper, onion, and carrot. Chop the broccoli into small florets so they cook quickly.
Heat the pan. Place a large skillet or wok over medium-high heat.
Add 1 tablespoon of oil and swirl to coat.
Cook the chicken. Add chicken in a single layer. Let it sear undisturbed for 2 minutes, then stir-fry until just cooked through and lightly browned, about 4–5 more minutes. Remove to a plate.
Stir-fry the vegetables. Add the remaining 1 tablespoon oil.
Add onion and carrot and cook 2 minutes. Add broccoli and bell pepper and cook 2–3 minutes more. Add the minced garlic and grated ginger; cook 30 seconds until fragrant.
Add the sauce. Give the teriyaki sauce a quick stir, then pour it into the pan.
Bring to a simmer, stirring, until it thickens and turns glossy, about 1–2 minutes.
Combine and finish. Return the chicken to the pan and toss to coat. Cook 1 minute to warm through. Taste and adjust with a splash of soy sauce for salt, or a drizzle of honey for sweetness.
Serve. Top with sliced green onions and sesame seeds.
Serve hot over rice or noodles.