Step 1

Place lily buds and mushrooms in a small bowl, and add very hot water to cover by 1 inch. Let soak until softened, about 30 minutes. Drain and rinse thoroughly. Trim and discard tough ends from buds, and cut in half crosswise. Coarsely chop mushrooms.

Step 2

Stir together lily buds, mushrooms, chicken stock, bamboo shoots, ginger, and salt in a large nonreactive saucepan over high. Cover and bring to a boil. Reduce heat to medium, and simmer 10 minutes. Stir in vinegar and red pepper; increase heat to medium-high, and boil mixture 2 minutes.

Step 3

Whisk together cornstarch and 3 tablespoons water in a small bowl. Whisk cornstarch mixture into chicken stock mixture in a slow, steady stream; cook 1 minute. Beat together egg and egg white in a medium bowl. Pour egg mixture into chicken stock mixture in a slow, steady stream, stirring gently. Stir in tofu, soy sauce, and sesame oil, and cook, stirring occasionally, until warmed, about 2 minutes. Sprinkle with scallions before serving.