Cook noodles
Cook noodles according to package instructions. Drain and set aside.
Prepare sauce
In a bowl, whisk soy sauce, oyster sauce, cornstarch, sugar, chicken broth, and sesame oil. Set aside.
Cook chicken
Heat oil in a wok or large skillet over medium-high heat. Add chicken and stir-fry until cooked through. Remove and set aside.
Cook vegetables
Add a bit more oil if needed. Stir-fry cabbage and carrots until crisp-tender.
Combine
Return chicken to the pan. Add cooked noodles and pour sauce over everything.
Toss & serve
Toss quickly until noodles are coated and sauce thickens. Finish with green onions and serve hot.