In a large skillet, heat the vegetable oil over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the broccoli, bell peppers, and carrots. Stir-fry the vegetables for about 3-4 minutes until they are tender but still crisp.
In a small bowl, whisk together the teriyaki sauce, soy sauce, honey, minced garlic, and minced ginger.
Return the cooked chicken to the skillet with the vegetables. Pour the sauce mixture over the chicken and vegetables, stirring to coat everything evenly. Cook for an additional 2-3 minutes until heated through.
Add the cooked egg noodles to the skillet and toss everything together until the noodles are well coated with the sauce. Cook for another minute to heat the noodles.
Serve hot, garnished with sesame seeds and sliced green onions if desired.