Whisk soy sauce, broth, rice vinegar, honey, cornstarch, sesame oil, red pepper flakes, and black pepper until smooth.
Pat chicken dry and slice thinly across the grain for quick cooking.
Heat a wok or large skillet over medium-high. Add 1 tablespoon neutral oil and swirl to coat.
Stir-fry the chicken in a single layer until just cooked, 3–4 minutes. Cook in two batches if crowded. Transfer to a plate.
Add remaining 1 tablespoon oil. Stir-fry onion and carrot for 2 minutes. Add garlic and ginger; cook 30 seconds until fragrant.
Add cabbage and toss constantly until crisp-tender, 3–4 minutes.
Return chicken and any juices. Stir the sauce and pour it in. Cook, tossing, until glossy and thickened, 1–2 minutes.
Remove from heat. Fold in green onions and sprinkle with sesame seeds. Serve immediately.