Boil ramen noodles for 1 minute less than the package indicates. Drain, rinse under cold water for 10 seconds, toss with 1 tablespoon vegetable oil, and set aside.
Heat the remaining oil in a large pan over medium heat. Sauté garlic and ginger for 2 minutes, then add bell pepper, broccoli, and mushrooms. Cook 3–5 minutes until crisp-tender.
Whisk soy sauce, Worcestershire sauce, ketchup, Sriracha, and brown sugar in a small bowl.
Season chicken lightly with salt and pepper. Push vegetables aside, add chicken, and cook 2–3 minutes until no longer pink outside.
Stir chicken and vegetables together and finish cooking the chicken through. Pour sauce over the mixture and toss to coat.
Add noodles and toss with tongs until coated and mixed with chicken and vegetables. Add sesame oil if using.
Garnish with sesame seeds, green onions, and cilantro if using. Serve immediately.