Soak shiitake and wood ear mushrooms in hot water for 1 hour until soft, then drain and slice thin.
Bring chicken broth to gentle boil, add sugar, salt, soy sauces, and sesame oil. Simmer 2 minutes.
Add sliced mushrooms, simmer 2 minutes.
Add tofu strips and bamboo shoots, return to simmer.
Mix cornstarch with water until smooth. Stir half into soup, add more if needed for desired thickness.
Create egg ribbons: stir soup in circular motion while slowly drizzling beaten egg.
Add white pepper and rice vinegar.
Adjust seasoning with additional vinegar, white pepper, and salt to taste.
Top with green onions and cilantro. Serve immediately.