Combine 4 chopped boneless skinless chicken breasts and 4 tablespoons corn starch in a large resealable bag and shake to coat.
Whisk together 6 tablespoons honey, 4 tablespoons ketchup, 3 tablespoons granulated sugar, 1 tablespoon brown sugar, 2 tablespoons white vinegar, 3 tablespoons soy sauce, and 1 teaspoon garlic powder and set aside.
Add 2 tablespoons olive oil to a large skillet, then add the coated chicken. Cook over medium heat for 5-6 minutes until browned.
Add 2 cups broccoli florets, and pour the sauce over the top. Continue to stir over medium heat for 4-5 minutes longer until chicken is cooked through.
In a small bowl, whisk together 2 tablespoons cornstarch and 2 tablespoons cold water . Pour the cornstarch mixture into the pan and stir until the sauce thickens. Sprinkle with sesame seeds, and serve.