Bring stock, mushrooms and bamboo shoots to boil in large saucepan. Reduce heat to medium-low; simmer 5 minutes. Stir in vinegar, soy sauce, sugar, ginger and white pepper.
Mix cornstarch and water in small bowl until smooth. Stir into saucepan with wire whisk. Gradually whisk in egg white; simmer until cooked through.
Ladle into soup bowls. Sprinkle with green onion and sesame seed.