Cook the noodles according to package directions until just al dente. Drain and rinse briefly under cool water to stop the cooking. Set aside.
Pat the chicken dry and season lightly with salt and pepper.
Heat 1 tablespoon of oil in a large skillet or wok over medium-high heat. Add the chicken and cook until it’s just cooked through, about 4–5 minutes. Transfer to a plate.
In the same pan, add the remaining tablespoon of oil. Sauté the garlic and ginger for about 30 seconds until fragrant.
Add the vegetables and stir-fry for 2–3 minutes, until they’re bright and crisp-tender.
Return the chicken to the pan. Stir in the soy sauce, oyster sauce, and chicken broth. Bring to a gentle simmer.
Stir in the cornstarch slurry and cook for another minute, until the sauce thickens slightly.
Add the noodles and toss to coat well with the sauce. Drizzle with sesame oil and mix in half of the green onions.
Taste and adjust with more salt, pepper, or soy sauce as needed. Serve hot, sprinkled with the remaining green onions.