Cut mushrooms into 1-inch diagonal slices. Cover mushrooms with water and l stand for 30 minutes. Remove mushrooms; cut off and discard stems. Thinly slice mushrooms and set aside.
Measure soaking water (discard any sandy portion at the bottom) and add enough stock to make a total of four cups liquid. Place in a two-quart pan and add sherry, bamboo shoots, and sliced mushrooms. Bring to a boil, then reduce heat; cover and simmer for 15 minutes.
Add tofu, peas, white vinegar, and soy; heat for three minutes. In a small bowl, stir together cornstarch and the 1/4 cup water. Add to soup and cook stirring, until slightly thickened. Turn off heat. Add pepper and sesame oil. Stirring continuously, slowly pour egg into soup. Sprinkle with onion; add salt to taste.