In a bowl, combine the sliced chicken with soy sauce, sesame oil, and cornstarch. Toss well and let it sit for at least 10 minutes while you prep everything else.
Whisk together all the sauce ingredients in a small bowl and set aside. Having this ready before you start cooking is a lifesaver — things move fast once that wok gets hot!
If using dried noodles, cook them according to the package directions until just barely done (they'll finish cooking in the wok). Drain and toss with a tiny drizzle of oil to prevent sticking.
Heat 1 tablespoon of vegetable oil in a large wok or skillet over high heat. Add the chicken in a single layer and cook for 3–4 minutes, flipping once, until golden and cooked through. Remove and set aside.
Add the remaining tablespoon of oil to the wok. Toss in the garlic and ginger, stirring quickly for about 30 seconds. Add the carrots, snap peas, and cabbage, and stir-fry for 2–3 minutes. You want the vegetables to still have a slight crunch.
Add the cooked noodles and the sauce to the wok. Use tongs to toss everything together over high heat for 2 minutes. Return the chicken to the pan, add the bean sprouts and green onions, and toss for another minute.
Plate up immediately and garnish with extra green onions and a drizzle of sesame oil if you like. Enjoy!