Marinate the Chicken - Cut the chicken against the grain into strips, about ¼-inch thick and 2-inch long. In a medium bowl, combine chicken, soy sauce, salt, cornstarch, and sesame oil. Set aside to marinate.
Make the Stir-fry Sauce - In a small bowl, whisk together the chicken broth, oyster sauce, soy sauce, sesame oil, and cornstarch. Set aside.
Boil the Noodles - In a large pot, bring water to a boil. Add dried noodles and cook according to the manufacturer’s directions until tender with some chew (al dente), about 2 to 3 minutes. Alternatively, if using fresh noodles, skip this boiling step. Drain into a colander and rinse with cold water to stop the cooking process. Drain well and set aside.
Stir-fry the Chicken - Heat a large wok, nonstick pan, or stainless steel pan over medium-high heat. Add 1 tablespoon vegetable oil. Once hot and shimmering, add the chicken in a single layer. Sear without moving until browned, about 30 seconds. Stir-fry until no longer pink, about 1 to 2 minutes. Transfer to a clean plate.
Add the Vegetables and Aromatics - Heat the wok over medium-high heat. Add 1 tablespoon vegetable oil. Once hot and shimmering, add the cabbage and carrots, and stir-fry until just tender, about 1 minute. Add in garlic and ginger, and stir-fry until fragrant, 20 seconds.
Add the Noodles and Sauce - Add the noodles and sauce. Toss and stir to combine. Cook until the sauce thickens and coats the noodles, about 1 minute. If using fresh noodles, cook until softened and tender, which may require a few additional minutes.
Add the Chicken and Bean Sprouts - Add the chicken, bean sprouts, and green onions, and stir-fry until just tender, 1 minute. Serve while still hot.
Notes
Noodle Substitution: Yakisoba, ramen, lo mein, thin wonton noodles, thin or regular spaghetti.
Using Fresh Noodles: Skip the boiling step and add directly to the wok for par-cooked fresh noodles. Raw fresh noodles need a few minutes of cooking, then drain well before adding. Toss in oil if sticking together too much.
Soy Sauce Substitutions: Use coconut aminos or tamari.
Oyster Sauce Substitutions: Hoisin sauce or teriyaki sauce. Alternatively, ¼ cup soy sauce and sugar (add 1 teaspoon of sweetener at a time, increasing to taste). A small amount of fish sauce can enhance the missing seafood taste, but use it sparingly, a ¼ teaspoon to start.
For Saucier Noodles: Double the sauce ingredients.
Storing: Cool completely and store in an airtight container for up to 3 days. Reheat in the microwave, covered, in 30-second intervals until hot.