Set a steamer basket in a medium pot with 1" water, cover pot, and bring water to a boil. Uncover and steam broccoli until crisp-tender, 5-6 minutes. Drain and set aside
Whisk cornstarch, pepper and 1 1/2 teaspoons salt in a large bowl. Add chicken and toss to coat
Heat 2 tablespoons olive oil in a large skillet over high. Add half of the chicken and cook, turning occasionally, until chicken is cooked through and a light brown crust forms, about 5 minutes. Transfer to a plate
Heat remaining olive oil, cook remaining chicken and transfer to a plate
Combine honey, soy sauce, vinegar, Sriracha, garlic, ginger, sesame oil, 1 tablespoon sesame seeds and 1/2 teaspoon salt in a medium bowl.
Transfer sauce to a skillet and cook 1 minute to reduce slightly.
Return chicken to skillet, toss in sauce to coat, and cook until sauce is reduced and thickened, about 2 minutes. Fold in reserved broccoli, toss to coat and remove from heat
Top with scallions and remaining sesame seeds. Serve with rice on the side