Rinse asparagus and break off the woody part of the stems. Cut into one inch pieces. Heat oil in large pan over medium heat. Add the leeks and cover tightly. Cook, stirring occasionally, until tender (about ten minutes). Add the broth, chopped asparagus and potato. Bring to boil over high heat. Return heat to low and simmer, partially covered, until potatoes are tender, about 30 minutes. Stir in milk and season to taste with salt and pepper. You can also use regular milk, it just won't be as thick. In batches, puree the soup in blender (or use a hand blender to do this in the pot). Return to pot and cook, stirring often, to heat through.

Makes 8 servings.