How to Make It
Place the trimmed asparagus in an ice bath for a minute first. This pre-treatment helps keep the green color.
Reserve as many asparagus tips as you would like as garnish and cook the asparagus pieces in a large pot of boiling salted water until very tender but still green, about 6 minutes. Drain.
Transfer the asparagus to a large bowl of ice water to stop the cooking process.
Working in batches, puree the remaining tips and pieces in a blender until smooth, adding about 3 tablespoons of the ice water to each batch to help form a puree. With the machine running, drizzle 1/3 cup extra virgin olive oil through the feed tube into the soup. Process until well blended. Season the soup to taste with fleur de sel.
Heat slowly in a pot and serve warm. (Note, the soup may be served chilled.)
Ladle the soup into 4 soup bowls. Cut the reserved asparagus tips lengthwise in half and float them atop the soup. Sprinkle each serving with a pinch of fleur de sel. Drizzle each serving with 1/2 teaspoon extra virgin olive oil and a dollop of Parmesan Custard (see Note). Serve immediately.