Cook the noodles according to package directions, drain, rinse if needed, and set aside.
In a medium bowl, whisk together cornstarch, chicken broth, soy sauce, oyster sauce, sugar, red pepper flakes, and sesame oil; set the sauce aside.
Heat 1 tablespoon vegetable oil in a wok or large deep nonstick skillet over medium-high heat until hot.
Add the chicken strips (work in batches if needed) and cook about 3–4 minutes per side until browned and cooked through; transfer to a plate.
Add the remaining 1 tablespoon oil to the pan, then add the matchstick carrots and sauté about 5 minutes.
Add the thinly sliced napa cabbage and red bell pepper and sauté 3–5 minutes until vegetables are crisp-tender.
Stir in diced green onions, minced garlic, and minced ginger and cook 1–2 minutes more until fragrant.
Toss the cooked noodles and reserved chicken into the pan, pour the sauce over everything, and toss to coat and heat through.
Serve warm, garnished with sesame seeds and additional green onions if desired.