Toss chicken in soy sauce, half of the sesame oil, and rice vinegar in a large bowl. Marinate for 20 minutes to 24 hours.
Mix all sauce ingredients in a bowl and set aside.
Heat the other half of the sesame oil in a large pan over medium high heat. Add marinated chicken and cook until browned on all sides. Remove pan from heat and set aside.
Add mushrooms, broccoli, and carrots to the pan and cook for 3-4 minutes. Stir frequently.
Add onion and bell pepper and cook for 2-3 minutes.
Add sauce and chicken and cook for 2-3 minutes.
Serve with rice or noodles, sprinkled with sesame seeds and red pepper flakes.