Cook noodles according to package directions until al dente. Drain, rinse, and set aside.
In a bowl, toss chicken slices with 2 tablespoons soy sauce and cornstarch. Let marinate for 10 minutes.
Heat vegetable oil in a large skillet or wok over medium-high heat. Cook chicken until golden brown and cooked through, about 5–6 minutes. Remove from skillet and set aside.
In the same skillet, add garlic, bell pepper, carrots, and broccoli. Stir-fry for 4–5 minutes until vegetables are tender-crisp.
Meanwhile, whisk together all sauce ingredients in a small bowl.
Return chicken to the skillet, add cooked noodles, and pour sauce over the top. Toss everything together until well coated and heated through.
Top with sliced green onions and serve hot.