Pour boiling water over top of mushrooms and let soak 15 to 20 minutes or until soft. Strain, saving liquid. Cut mushrooms into slices, cutting off tough stems.
Add broth, mushrooms, saved liquid, bamboo, vinegar, tamari, ginger root, and sugar to a large pot. Let boil. Lower heat and let simmer 10 minutes. Heat again and stir in cornstarch and water. Keep boiling until thick, about 1 minute, stirring frequently.
Mix in tofu, place lid on pot, and simmer 5 minutes. Sprinkle with salt and peppers. When ready to serve, whisk in egg and sesame oil.
Make sour sauce by whisking together the last three ingredients.
Spoon soup into individual bowls and top with sour sauce and green onions.