In a medium bowl, combine 2 tablespoons of the soy sauce, rice vinegar, and 2 teaspoons of the sugar.
Add chicken and toss to coat. Let marinate at room temperature for 20 minutes or cover and chill for 1 hour.
Meanwhile, cook noodles according to package directions and drain. Rinse with cold water and drain well.
For sauce, in a small bowl, stir together chicken broth, the remaining 4 tablespoons soy sauce, the remaining 2 teaspoons sugar, and the cornstarch.
In a 10-inch skillet or a wok, heat vegetable oil and sesame oil over medium-high heat. Add garlic and cook for 30 seconds. Add carrots and cook for 2 minutes. Add bok choy and green onions, cook for 2 minutes. Remove vegetables from wok.
Drain chicken and discard marinade. Add chicken to wok (add more oil if necessary) and cook until no longer pink (about 3 or 4 minutes).
Push chicken from the center of the wok. Stir sauce and add to center of the wok. Cook and stir until thickened and bubbly.
Add the cooked noodles and vegetables. Toss the mixture until combined and heated through.
Transfer to a platter and serve.
Notes
This recipe is so flexible, use whatever vegetables you like or have on hand.
Chop the vegetables and cut up the chicken ahead of time during a meal prepping session for an even easier meal on a busy night.
This recipe doubles well if you are cooking for a crowd.
Leftovers are fabulous and can be reheated in the microwave, on the stove top, or even in the toaster oven.