Mix the sauce. In a bowl, whisk soy sauce, dark soy (if using), oyster sauce, hoisin (if using), sugar, vinegar, chicken broth, cornstarch, and white pepper. Set aside.
Prep the chicken. Slice chicken into thin strips against the grain.
Pat dry and toss with a pinch of salt, pepper, and 1 teaspoon cornstarch for extra tenderness.
Cook the noodles. Boil lo mein noodles according to package instructions until just tender. Drain and rinse quickly under cold water to stop cooking. Toss with 1 teaspoon sesame oil to prevent sticking.
Heat the pan. Set a large skillet or wok over medium-high heat.
Add 1–2 tablespoons oil until shimmering.
Stir-fry the chicken. Add chicken in a single layer. Cook 3–4 minutes, stirring once, until lightly browned and cooked through. Transfer to a plate.
Sauté aromatics. Add a bit more oil if needed.
Stir-fry garlic and ginger for 20–30 seconds until fragrant. Don’t let them burn.
Cook the vegetables. Add bell pepper, carrots, and snap peas. Stir-fry 2–3 minutes until crisp-tender.
Add cabbage and half the green onions; cook 1 minute more.
Combine everything. Return chicken to the pan. Add cooked noodles and pour in the sauce. Toss with tongs for 1–2 minutes, letting the sauce thicken and coat the noodles.
Finish and serve. Turn off heat.
Drizzle 1–2 teaspoons toasted sesame oil and toss. Top with remaining green onions, sesame seeds, or chili crisp if you like.