Trim the tough, woody ends off the asparagus. Snap them where they naturally break. Cut the remaining stalks into 1-inch pieces. Blanch the reserved asparagus tips in boiling salted water for 1-2 minutes until bright green and tender-crisp. Immediately transfer to an ice bath to stop cooking, then drain and set aside for garnish.

In a large pot or Dutch oven, heat the olive oil over medium heat. Add the chopped onion and cook for 5-7 minutes, stirring occasionally, until softened and translucent. Add the minced garlic and cook for another minute until fragrant, being careful not to brown it.

Add the 1-inch asparagus pieces (excluding the reserved tips) and vegetable broth to the pot. Bring to a gentle boil, then reduce heat to a simmer, cover, and cook for 10-15 minutes, or until the asparagus is very tender.

Carefully blend the soup until completely smooth using an immersion blender directly in the pot. If using a standard blender, transfer the soup in batches to avoid overfilling, blending until smooth, then return to the pot. For an exceptionally smooth soup, pass it through a fine-mesh sieve, pressing on any solids, then return to the pot.

Stir in the heavy cream and fresh lemon juice. Season with salt and freshly ground black pepper to taste. Heat gently for a minute or two, but do not boil after adding the cream.

Ladle the hot soup into bowls. Garnish each serving with a few blanched asparagus tips, a drizzle of extra heavy cream, chopped fresh chives, or croutons, if desired. Serve immediately.