Boil a pot of water and cook the asparagus until tender crisp, about 3 minutes. Drain, rinse under cold water, and drain again; set aside.
In the meantime, in a separate large pot, bring the broth to a boil. In a cup, whisk together the water and cornstarch until smooth. Whisk cornstarch mixture into the broth and let simmer until it thickens slightly, about 2 minutes.
Lower the heat so that the broth barely simmers. Slowly pour the eggs into the soup, while stirring quickly and in a circular motion; let cook for about 1 minute. Stir in the soy sauce, vinegar, and pepper.
Evenly divide asparagus into 4 and place into a soup bowl. Top with 1 1/4 cups of soup.