Asparagus-Potato Soup

PLACE ALL THE INGREDIENTS except cheese in a large saucepan. Bring the liquid to a simmer over moderate heat, then adjust the heat so that it bubbles gently. Cover the pot and simmer the broth for 30 to 35 minutes, until the vegetables are very tender. Cool the broth, still covered, for 20 minutes. Puree the broth and the vegetables in batches, in a blender or in a food processor fitted with the metal chopping blade. Return the puree to the saucepan, set it over moderate heat and bring the soup just to serving temperature. Ladle the soup into heated bowls and top each portion with 1 tablespoon of the Parmesan cheese.