Slice the chicken breasts into thin strips. Wash and slice the bell peppers, separate broccoli into small florets, julienne the carrot, and chop the green onions. Gently loosen yakisoba noodles if packaged in a block.
Heat vegetable oil in a large skillet or wok over medium-high heat. Add chicken strips, season with salt and pepper, and stir-fry for 4-5 minutes until cooked through and lightly browned. Remove chicken and set aside.
In the same skillet, add more oil if needed. Stir-fry bell peppers, broccoli, and julienned carrot for 3-4 minutes until tender but still crisp.
Return cooked chicken to skillet with vegetables. Add yakisoba noodles and pour teriyaki sauce over everything. Toss well and heat through to allow noodles to absorb sauce.
Drizzle sesame oil over the yakisoba and sprinkle toasted sesame seeds on top. Stir in chopped green onions, reserving some for garnish if desired.
Serve the Teriyaki Chicken Yakisoba hot, directly from the pan. Enjoy as a filling meal or with simple sides.