Whisk soy sauce, honey, rice vinegar, sesame oil, garlic, and ginger in a bowl; set aside.
Heat oil in a large skillet over medium-high heat. Add chicken, season lightly with pepper, and cook until browned and nearly cooked through, 5–6 minutes.
Add broccoli to the pan with a splash of water, cover, and steam 3 minutes until bright and crisp-tender.
Pour sauce over chicken and broccoli; simmer 1–2 minutes. Stir in cornstarch slurry and cook until sauce thickens and coats everything.
Serve over warm brown rice; top with sesame seeds and green onions.