Steam broccoli with salt until bright green and tender-crisp, about 6 minutes. Rinse with cold water to stop cooking.
Whisk soy sauce, water, sesame oil, honey, vinegar, ginger, garlic, sesame seeds, and cornstarch until smooth.
Toss chicken in a bag with cornstarch, flour, salt, and pepper until evenly coated.
Sauté chicken in hot olive oil over medium heat until golden and fully cooked on all sides.
Pour sauce into the skillet, stir, and simmer for 2–3 minutes until thick and glossy.
Fold in the broccoli, garnish with green onions, and serve warm.