Cook the chow mein or yakisoba noodles according to package instructions, drain, rinse under cold water if directed, and set aside.
In a medium bowl, whisk together cornstarch, chicken broth, soy sauce, oyster sauce, sugar, red pepper flakes, and sesame oil until smooth; set the sauce aside.
Heat 1 tablespoon vegetable oil in a wok or large deep nonstick skillet over medium-high heat until hot but not smoking.
Add the chicken strips (work in batches if necessary) and cook 3–4 minutes per side until browned and just cooked through; transfer to a plate.
Reduce heat slightly and add the remaining 1 tablespoon oil. Add the matchstick carrots and sauté for about 5 minutes until they begin to soften.
Add the napa cabbage and red bell pepper and sauté 3–5 minutes until crisp-tender.
Stir in the diced green onions, minced garlic, and minced ginger and cook 1–2 minutes more until fragrant.
Return the chicken and the cooked noodles to the wok, pour the prepared sauce over everything, and toss well to coat and heat through, about 1–2 minutes.
Serve warm, garnished with sesame seeds and additional sliced green onions if desired.
