Add all sauce ingredients to a small pot and bring to a boil over medium heat. Lower heat to a simmer for another 10 minutes. Allow to cool slightly.
Marinate chicken in 1/3 of the teriyaki sauce for at least 1 hour. Reserve remaining sauce in the refrigerator.
Cook rice according to package directions. Divide evenly among 4 serving dishes. Set aside.
Add broccoli to a large microwave safe bowl. Cover with a very damp paper towel and microwave for 2 minutes or until broccoli is bright green. Divide evenly among serving dishes. Set aside.
Heat skillet over medium-high heat again. Add marinated chicken (with the marinade) and cook covered for 2-3 minutes. Remove cover and flip chicken, covering again for about 1 minute. Uncover and allow marinade to reduce as chicken finishes cooking through. Add remaining teriyaki sauce on top of chicken and mix.
Divide chicken evenly among serving dishes. Top with sesame seeds, if desired.