Cook noodles according to package directions until just al dente; drain and toss with a little oil to prevent sticking.
Mix soy sauce, oyster sauce, dark soy (if using), rice vinegar, sesame oil, sugar and chicken broth in a bowl; set aside.
Toss sliced chicken with a pinch of salt and a teaspoon of cornstarch for a light velveting.
Heat 1 tbsp oil in a wok or large skillet over high heat until shimmering.
Add chicken in a single layer; stir-fry until just cooked through (2–3 minutes); remove to a plate.
Add remaining oil, then sauté garlic and ginger for 20–30 seconds until fragrant.
Add carrots and cabbage (or bok choy); stir-fry 1–2 minutes until slightly softened.
Return chicken to the wok, add bean sprouts and half the scallions; toss to combine.
Pour sauce mixture over everything and bring to a simmer.
Add cooked noodles and toss vigorously to coat; if sauce is thin, stir in cornstarch slurry and cook until sauce thickens.
Adjust seasoning with more soy or a pinch of sugar as needed, finish with remaining scallions and sesame seeds, and serve immediately.