Cut away the stem of the cabbage and discard. Cut the cabbage lengthwise in half, then cut each half lengthwise in half again. Cut each quarter into 1 1/2-inch sections, separating the leafy sections from the stem pieces, and place in a bowl. Cut each leek half into thin slices, about 1/4 inch thick. Prepare all the remaining ingredients and place near the stove.
Heat the oil in a large, heavy pot over medium-high heat until hot, about 25 seconds. Add the leeks and ginger and stir-fry until fragrant, about 15 seconds. Add the tougher sections of the cabbage and the mushrooms and toss lightly for 1 to 2 minutes, until slightly softened.
Add the rice wine, partially cover, and reduce the heat slightly. Cook for about 5 minutes, until tender and dry. Add the leafier sections of the cabbage, the tofu slices, and the broth and bring to a boil. Lower the heat slightly and simmer for 15 minutes.
Slowly add the cornstarch and water mixture, stirring constantly to prevent lumps. Cook over medium-high heat until the broth has thickened, 3 to 4 minutes. The soup should have the consistency of heavy cream. Stir in the black vinegar, soy sauce, sesame oil, salt, and black pepper; taste for seasoning, adding more soy sauce if necessary. Turn off the heat and slowly add the egg, pouring it in a thin stream around the circumference of the pot. Stir the soup several times.
Ladle the hot soup into bowls, and serve immediately.
Variations: Add 1 cup shredded carrots for extra color and 1 teaspoon crushed red pepper flakes for additional spiciness. Substitute 6 to 8 dried black mushrooms or 1 1/4 ounces dried porcini mushrooms for the fresh shiitakes. Rinse and soften in hot water to cover, reserving the broth. (You can extend the broth with additional water and use in place of vegetable broth or add to chicken broth for extra flavor.) Trim the mushroom stems or tough ends, discard, and use the caps as above.
Reprinted from: Simple Asian Meals (c) 2012 by Nina Simonds. Permission granted by Rodale, Inc. Available wherever books are sold.