Combine cornstarch and water in a small bowl, stirring with a whisk.
Combine cornstarch mixture, broth, sherry, soy sauce, ginger, and oil in a large saucepan. Bring to a boil. Add mushrooms and carrot; cook 2 minutes. Add peas and shrimp; cook 3 minutes or until shrimp are done. Remove from heat. Slowly drizzle egg into broth mixture, stirring constantly. Stir in onions.