Heat the oil in a large skillet or wok over medium heat. Season the chicken with salt and pepper, then cook until lightly browned and cooked through. Remove from the pan and set aside.
Add the garlic, carrots, celery, mushrooms, cabbage and onion to the same pan. Sauté for about 5 minutes, until they begin to soften.
Pour the chicken broth into the skillet and bring to a gentle boil. Add the noodles (uncooked) and cook for about 2 minutes. (Flipping throughout if necessary to evenly soak up the broth.
Return the chicken to the pan. Add the soy sauce, umami sauce and black pepper. Toss everything together until evenly coated.