Combine 2 tablespoons soy sauce, rice vinegar, and 2 teaspoons sugar in a medium bowl. Add the chicken and toss to coat. Let marinate for 20 minutes at room temperature.
Cook the noodles according to package directions and set aside.
In a small bowl, combine the broth, cornstarch, remaining 4 tablespoons soy sauce, and remaining 2 teaspoons sugar. Set aside.
In a wok or a large skillet, heat the vegetable and sesame oil. Add the garlic and cook for about 30 seconds, stirring. Add the carrot, bell pepper, celery and cook for 2-3 minutes more, stirring. Remove the veggies from a skillet.
Drain the chicken, discarding the marinade, and add it to the same wok / skillet. Add more oil, if necessary, and cook for 3-4 minutes until no longer pink. Stir in the broth based sauce and cook, stirring, until thickened. Add the cooked noodles and prepared veggies. Toss the mixture using two spatulas until combined. Serve sprinkled with some chopped scallions over the top. Enjoy!