Soak dried mushrooms in hot water until they have reconstituted (about 20 - 30 minutes)
Squeeze out any excess water from the mushrooms, then cut into thin slices.
Mix cornstarch with ½ cup water. Stir well, then set aside.
Bring chicken stock to a boil in a large pot over medium-high heat.
In a small bowl, combine apple cider vinegar, soy sauce, sesame oil, dark soy sauce and brown sugar. Pour this sauce mixture into the pot of chicken stock.
Add the sliced mushrooms to the soup, followed by the bamboo shoots.
Give the cornstarch mixture a good stir, then pour it into the soup. Stir the soup immediately to allow the cornstarch to thicken the soup evenly.
Add Szechuan chili oil to the soup (if you prefer a non-spicy soup, omit this step).
Pour the beaten eggs into the soup in a slow, steady stream.
While pouring the eggs into the soup, use a pair of chopsticks to swirl the soup. Swirl quickly to get a thin, silky egg consistency, or swirl slowly to get a chunkier texture.
Add the diced tofu and the ground white or black pepper to the soup.
Stir to combine all ingredients, then transfer to serving bowls.