Step 1In a small bowl, whisk Worcestershire sauce, soy sauce, ketchup, oyster sauce, and sugar; set aside.
Step 2Generously season chicken with salt and black pepper. In a large, heavy skillet or wok over medium-high heat, heat 2 Tbsp. oil. Add chicken and cook, turning occasionally, until browned and just cooked through, about 7 minutes. Transfer chicken to a plate.
Step 3In same skillet over medium heat, heat remaining 1 Tbsp. oil. Cook onion and carrots, stirring occasionally, until just softened, about 5 minutes. Add cabbage, scallion, and bean sprouts. Cook, stirring, until cabbage is slightly wilted and some vegetables are browned, 4 to 5 minutes; season with salt and pepper.
Step 4Meanwhile, prepare noodles according to package directions; reserve seasoning packets for another use. Make sure noodles are thoroughly drained.
Step 5Add noodles to skillet and toss to combine. Return chicken and any accumulated juices to skillet and toss again to combine. Cook, stirring, until noodles start to brown, 2 to 3 minutes more.
