To a wok over medium heat, add the oil, star anise, ginger slices, and white parts of the scallion. Cook for 1 minute, then add the garlic, mushrooms, and carrot. Stir-fry for 1 minute.
Increase the heat to high. Add the Shaoxing wine, followed by the napa cabbage. Stir-fry until the cabbage just starts to wilt, about 30 seconds, and then add the rice cakes and water. Cover, and cook over medium heat for 2 minutes.
Uncover the wok, and stir. With the heat still at medium, add the vegetarian oyster sauce, light soy sauce, dark soy sauce, sugar, sesame oil, and white pepper. Give everything a stir again.
Increase the heat to high, and finally, add the bean sprouts and the green parts of the scallions.
Stir-fry everything together for 1 final minute, until the rice cakes are tender but still chewy, and the scallion greens are just wilted. Plate and serve!