In a small bowl, combine the cornstarch, soy sauce, ginger and 1/2 cup cold water; set aside., In a large saucepan, combine broth and remaining water. Bring to a simmer; add noodles. Cook, uncovered, for 15 minutes. Add broccoli and carrot; simmer until noodles are tender, 3-4 minutes longer., Drizzle beaten egg into hot soup, stirring constantly. Stir cornstarch mixture and add to the pan. Bring to a boil; cook and stir until slightly thickened, about 2 minutes. Add shrimp; heat through.