Cook the noodles: Bring a large pot of salted water to a boil. Cook noodles according to package directions until just shy of tender. Drain, rinse briefly under cool water to stop cooking, and toss with a teaspoon of oil to prevent sticking.
Make the sauce: In a small bowl, whisk soy sauce, oyster sauce, dark soy (if using), hoisin (if using), sesame oil, sugar or honey, chicken broth, cornstarch, and pepper.
Set aside.
Prep the chicken: Pat the chicken dry and slice thinly against the grain. Season with a pinch of salt and pepper. For extra tenderness, you can “velvet” it by tossing with 1 teaspoon cornstarch and 1 teaspoon soy sauce.
Heat the pan: Place a large skillet or wok over medium-high heat.
Add 1 tablespoon oil and swirl to coat until shimmering.
Stir-fry the chicken: Add chicken in a single layer. Cook without moving for 1–2 minutes to get light browning, then stir-fry until just cooked through, 3–4 minutes total. Transfer to a plate.
Cook aromatics: Add another teaspoon of oil if needed.
Add garlic and ginger. Stir for 20–30 seconds until fragrant, being careful not to burn.
Stir-fry the vegetables: Add carrots, bell pepper, and peas. Cook 2–3 minutes until crisp-tender.
Add cabbage and most of the green onions (save some for garnish). Stir-fry 1–2 minutes more.
Combine noodles and chicken: Return chicken to the pan with the vegetables. Add the cooked noodles, breaking up any clumps with tongs.
Add the sauce: Pour the sauce around the edges of the pan.
Toss everything together over medium-high heat until the noodles are coated and glossy and the sauce slightly thickens, about 1–2 minutes.
Finish and serve: Taste and adjust seasoning with a splash more soy sauce, a pinch of sugar, or a few drops of sesame oil. Garnish with remaining green onions. Serve hot.