Place the dried shiitake and wood ear mushrooms in separate bowls and soak them in lukewarm water. The shiitake mushrooms will take about 1 hour to fully rehydrate, while the wood ear mushrooms will soften in 10-15 minutes. Once rehydrated, slice them thinly.
In a large pot over medium heat, heat the chicken broth until it reaches a low boil. Add shiitake mushrooms, wood ear mushrooms, and bamboo shoots and simmer for 5 minutes. Then add the ginger, soy sauce, dark soy sauce, sugar, rice vinegar, salt, white pepper, and sesame oil. Bring to a low boil and let it cook for 2–3 minutes to allow the flavors to meld together.
Stir the cornstarch slurry (cornstarch mixed with water) into the soup. Simmer for another 1-2 minutes, or until the broth slightly thickens. Reduce the heat to a gentle simmer, then slowly drizzle in the beaten eggs while continuously stirring the soup in a circular motion with chopsticks or a wooden spoon. This will create delicate egg ribbons. Let the eggs set for about 1 minute.
Gently add the tofu and chopped green onions and simmer for another minute. Taste and adjust seasoning if needed. Serve hot and enjoy!