Remove and discard roots, tough outer leaves, and tops from leeks; wash leeks thoroughly, and coarsely chop.
Sauté leeks, celery, and onion in butter in a large Dutch oven 10 minutes or until tender. Stir in potatoes, chicken broth, rosemary, and salt; cover and bring to a boil. Reduce heat to low, and cook 20 minutes.
Stir in whipping cream, and heat to serving temperature. (Do not boil.) Serve hot in individual soup bowls, and garnish with chopped parsley.