How to Make It
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.
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.
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.
Find dried lily buds and dried tree ear mushrooms at Asian markets.