1. In a medium bowl, whisk together 3 tablespoons soy sauce, 2 teaspoons sesame oil, and 2 teaspoons honey.

2. Add the chicken, toss to coat, and marinate for 20 minutes.

3. Heat 2 teaspoons canola oil in a large nonstick skillet over medium-high heat.

4. Remove the chicken from the marinade with a slotted spoon and discard the marinade.

5. Add half of the chicken to the pan and cook until browned and cooked through, turning once or twice, about 6 minutes. Transfer the chicken to a large serving platter.

6. Repeat with 2 more teaspoons of canola oil and the remaining chicken. Transfer to the serving plate.
 
7. Add the broccoli to the pan along with 2 tablespoons water, cover and steam for 4 minutes.

8. Create a hole in the broccoli by pushing it aside and heat the remaining 2 teaspoons canola oil in the skillet over medium-high heat. Add the scallions, ginger, and garlic and cook, stirring until fragrant, 1 to 2 minutes.

9. In a small bowl, whisk together the broth, the remaining 2 tablespoons soy sauce, the remaining 3 teaspoons honey, the cornstarch, vinegar, and chili paste until the cornstarch and honey are dissolved. Add the mixture to the pan and cook, stirring, until the mixture is thickened and darkened in color, 2 to 3 minutes.

10. Stir in the remaining 2 teaspoons sesame oil.

11. Pour the sauce and broccoli mixture over the chicken. Sprinkle with the sesame seeds and 2 tablespoons scallion greens. Serve with brown rice, if desired.