Add the roughly chopped carrot to the food processor and pulse until very finely chopped. Remove to a bowl. Repeat with the napa cabbage, then the mushrooms.

Heat the oil in a wok over medium heat. Add the ginger and garlic, and cook for 20 seconds. Add the mushrooms, and cook for 2 minutes, until fragrant. Add the napa cabbage and carrot, and cook until totally wilted, about 3 minutes. Remove this mixture to a large mixing bowl.

Mash the tofu well, and add it to the vegetable mixture, along with the scallions, vegetarian oyster sauce, Shaoxing wine, soy sauce, sugar, sesame oil, salt, and white pepper. Mix well.