In a medium bowl, combine the soy sauce, sesame oil, sesame seeds and ginger. Add the chicken and season with pepper. Marinate, refrigerated, for 45 minutes.
Meanwhile, preheat the oven to 425 degrees F. Once hot, put a baking sheet lined with foil in the oven for 20 minutes to heat up.
Toss the marinated chicken with the onion, carrots, bell pepper and broccoli, then drain any excess liquid. Put the chicken and vegetables flat on the hot baking sheet and season with salt and pepper. Put the baking sheet back in the oven and roast, stirring halfway through to promote even browning, until the chicken is fully cooked, 12 to 14 minutes.
Transfer the chicken and vegetables to a platter and top with the scallions.