Cook the noodles according to package directions (be sure not to over-cook). Drain and set aside.
While noodles are cooking, prepare the sauce: In a small bowl whisk all the sauce ingredients together. Set aside.
Add 2 tablespoons of sauce to the chicken. Set aside.
Heat the 1 tablespoon of oil in a large wok or skillet over medium heat. Add the chicken and cook for about 5 minutes, or until the chicken starts to brown and is no longer pink. Transfer chicken to a plate and set aside.
Add the other 2 tablespoons of oil to the wok. Add the garlic, ginger, carrots, mushrooms, and red pepper; cook for a 2 - 4 minutes, until tender, while tossing around. Stir in snow peas and bok choy and cook until the bok choy has wilted, about 2-3 minutes.
Stir in cooked egg noodles and cooked chicken. Add ½ cup sauce mixture and ¼ cup of water, and gently toss to combine. Stir fry for 1 – 2 minutes. Add the scallions and cook for 1 more minute.
Garnish more scallions and black sesame seed, if desired. Serve immediately.