How to Make It
Heat the olive oil in a medium saucepan. Add the leeks and cook over moderately low heat, stirring often, until softened, about 6 minutes. Add the stock, season with salt and pepper and bring to a boil. Add the asparagus stems and cook over moderately low heat until tender, about 6 minutes. Add the spinach and cook for 3 minutes.
Puree the soup in a blender. Refrigerate until chilled, at least 2 hours or overnight. Season with salt and pepper.
Cook the asparagus tips in a medium saucepan of boiling salted water until barely tender, about 4 minutes. Drain and rinse in cold water. Drain again and pat dry. Ladle the soup into bowls and garnish with the asparagus tips, yogurt and flowers.