In small bowl, soak dried mushrooms in hot water for 20 minutes or until softened. Cut off stems and any hard areas and discard. Cut caps into thin slices. Set aside.
In stock pot, heat canola oil over medium-high heat. Add mushrooms and carrots and cook 2 minutes or until carrots are just soft. Add vegetable broth and bamboo shoots and bring to a boil. Add cornstarch mixture and stir until soup thickens, about 2 minutes. Add soy sauce, rice vinegar and white pepper. Stir.
Add tofu and bring soup back to a boil. While stirring soup in circular motion in one direction, pour eggs in thin stream into soup.
Remove soup from heat. Stir in green onions. Taste and adjust avour with rice vinegar and white pepper.