Thaw shrimp, if frozen. In a large saucepan combine chicken broth, mushrooms, vinegar, soy sauce, sugar, ginger, and pepper. Bring to boiling; reduce heat. Simmer, covered, for 2 minutes. Stir in shrimp and tofu. Return to boiling; reduce heat. Simmer, covered, for 1 minute more.
Stir together cornstarch and cold water; stir into chicken broth mixture. Cook and stir until slightly thickened and bubbly. Cook and stir for 2 minutes more. Stir in peas, carrot, and green onion. Pour egg into the soup in a steady stream, stirring a few times to create shreds.