Begin by boiling water in a pot. Once boiling, add the noodles and cook according to package instructions until al dente. Drain and set aside.
In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the sliced chicken and season with a little salt and pepper. Stir-fry for about 5-7 minutes until the chicken is cooked through and golden brown.
Add the minced garlic and ginger to the skillet, stirring for about 30 seconds until fragrant.
Toss in the sliced bell pepper, julienned carrot, and broccoli florets. Stir-fry for another 3-4 minutes until the vegetables are tender but still crisp.
In a small bowl, mix together the soy sauce, oyster sauce, cornstarch, water, and sesame oil. Pour this sauce over the stir-fry and stir well to coat the chicken and vegetables.
Add the cooked noodles to the skillet and toss everything together until well combined and heated through, about 2 minutes.
Taste and adjust seasoning with more salt, pepper, or soy sauce if needed.
Serve hot, and garnish with green onions and sesame seeds if desired.