- Trim asparagus and cut into 2-inch lengths.
- Heat olive oil in large saucepan over medium heat. Add leeks and cook, stirring, until softened, about 5 minutes. Add broth, asparagus, potato, thyme sprigs, salt, and pepper. Cover and bring to boil. Reduce heat and simmer, covered, until vegetables are fork-tender, about 20 minutes. Discard thyme sprigs. Let soup cool about 5 minutes.
- Puree soup, in batches, in blender. Transfer to large bowl and let cool to room temperature. Stir in half-and-half; cover and refrigerate until well chilled, at least 4 hours or up to 2 days.
- Ladle soup evenly into 6 bowls. Drizzle with extra-virgin olive oil and sprinkle with chive ﬂowers (if using).
- Per serving: 1 cup
For an additional garnish, trim 18 pencil (thin) asparagus and cut into 4- to 5-inch lengths (reserve bottoms of stalks for another use). Bring 1/2 inch of water to a boil in a large skillet. Add the asparagus and cook, covered, just until tender, about 2 minutes. Drain and rinse under cold water. Place 3 asparagus in each bowl of soup, then garnish with oil and chive ﬂowers as directed.