In a medium Dutch oven, heat oil over medium-high heat. Add asparagus and ¼ teaspoon salt; cook, stirring occasionally, for about 3 minutes. Add broth, and bring to a boil over medium-high heat; reduce heat, and simmer, stirring occasionally, until tender, about 5 minutes. Reserve ⅓ cup asparagus mixture.

In the container of a blender, place remaining asparagus mixture, cream, avocado, chives, lemon juice, pepper, and remaining ½ teaspoon salt; process until smooth.

Return soup to Dutch oven, and cook until heated through. Top with reserved ⅓ cup asparagus mixture and garnish with oil, if desired.