Steam broccoli, covered, until crisp-tender, 5–6 minutes. Drain and set aside.
Whisk cornstarch, pepper, and 1 1/2 tsp. salt in a large bowl. Add chicken and toss to coat.
Heat 2 Tbsp. vegetable oil in a large NON-STICK skillet over high. Add half of the chicken and cook, turning occasionally, until chicken is cooked through and a light brown crust forms, about 4-5 minutes.
In a medium saucepan whisk together honey, worcestershire, coconut aminos, Sriracha, garlic, ginger, sesame oil, 1 Tbsp. sesame seeds, and remaining 1/4 tsp. salt. Bring to a boil and reduce heat to simmer for 4-5 minutes. Meanwhile, whisk together 1 TBS cornstarch and warm water in a small bowl. Add to mixture and stir. Allow sauce to continue simmers for 4 minutes until thick. Remove from heat and set aside.
Transfer the first batch of chicken to a plate. Heat remaining 2 Tbsp. vegetable oil and cook remaining chicken.
Add sauce to skillet along with the first batch of chicken. Toss well, about 2 minutes. Fold in reserved broccoli, toss to coat, and remove from heat.
Cook rice according to package e and add into a large bowl. Top rice with Sesame Chicken and Broccoli.
Garnish with remaining sesame seeds and chopped scallions.