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.
Heat half of sesame oil in a large skillet over medium-high heat. Add half of shallots and sauté until fragrant. Add half of the halved baby bok choy heads, cut side down. Add half of the soy sauce and cover immediately.
Cook bok choy, covered, for 1 minute, then remove cover and flip. Continue cooking, uncovered for another 2 minutes before removing from skillet. Repeat process with remaining baby bok choy. Set aside.
Cook basmati rice in pouch according to package directions. Divide evenly among 5 serving dishes. Divide cooked bok choy evenly among 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 about half of remaining teriyaki sauce on top of chicken and mix.
Divide chicken and remaining teriyaki sauce evenly among serving dishes. Top with sesame seeds, if desired.