1. Rinse cloud ears and lily buds under cool running water. Place in a small bowl, cover with cool water, and soak until soft, 15 to 20 minutes; drain. Pinch out and discard any hard spots from cloud ears, then rinse again; tear ears into 1/2-inch pieces. Remove and discard hard ends from lily buds; tie a knot in the center of each bud.
2. While cloud ears and lily buds are soaking, rinse and drain tofu; cut into 1/2-inch cubes. Rinse pork and pat dry; cut into 1/4-inch-thick matchstick-size pieces about 2 inches long. Rinse and drain bamboo shoots; cut lengthwise into 1/4-inch-wide strips.
3. In a 3- to 4-quart pan over high heat, bring broth and ginger to a boil; reduce heat, cover, and simmer to blend flavors, 20 to 25 minutes. Remove and discard ginger.
4. Stir in cloud ears, lily buds, tofu, pork, and bamboo shoots and bring to a boil over high heat. In a small bowl, mix cornstarch and vinegar until smooth; stir into boiling broth mixture and continue stirring until it boils again, 1 to 2 minutes.
5. In a small bowl, beat egg with a fork to blend. Remove soup from heat; immediately stir in egg, green onions, sugar, and pepper. Pour into a large bowl.