Put the mushrooms and black fungus into two separate bowls, cover with cold water, and soak for at least 20 minutes, or until softened. Drain both. Remove the mushrooms, squeeze dry, and discard the stems. Thinly slice, then set aside. Tear the black fungus into small pieces.
Combine the pork, 1/4 teaspoon salt, and the cornstarch (cornflour) in a bowl and set aside.
In a separate bowl, combine the tofu, 1/4 teaspoon salt, and enough cold water to cover and soak for 15 minutes. Drain, cut into thin strips, and set aside.
Bring 4 1/4 cups (34 fl oz/1 liter) water to a boil in a large saucepan and add 1 teaspoon salt and the sugar. Put in the mushrooms, black fungus, and bamboo shoots. Drop the pieces of pork, using chopsticks to gently disperse them to prevent sticking. Do not stir.
Mix the water chestnut flour with 4 tablespoons water in a small bowl, stir until dissolved, and pour slowly into the soup, stirring continuously. Add the tofu and reduce to medium-low heat.
Hold a strainer (sieve) over the soup and slowly pour the beaten eggs into the strainer. At the same time, move the strainer in a circular motion over the soup so that the beaten egg is strained into the soup in a continuous line. Let sit for 1 minute, do not stir.
Stir in the vinegar and white pepper, then add the sesame oil. Divide the noodles, if using, among the bowls. Ladle over the hot soup and garnish with cilantro (coriander), if using. Serve.
Adapted from China: The Cookbook by Kei Lum and Diora Fong Chan (Phaidon, 2016)