Place all ingredients but the cheese in a medium size saucepan and bring to a boil over low heat until the asparagus, the potato and the onion are very tender. Remove from heat, cover pan and cool for 30 minutes. Blend or process until a soft puree is obtained. Force through a strainer if necessary and correct seasoning. Some milk or cream may be added if desired.
Heat before serving and sprinkle with parmesan cheese.