Prepare the vegetables by washing the asparagus and snapping off the woody ends. Cut the tender spears into one-inch pieces, keeping the tips separate for garnish. Slice and wash the leeks.

Heat olive oil in a large pot over medium heat. Add leeks and a pinch of salt, sauté for 5-7 minutes until soft. Add minced garlic and cook for another minute.

Add chopped asparagus stalks to the pot, stir for 2 minutes. Pour in vegetable broth and bring to a gentle boil. Reduce heat and simmer for 8-10 minutes until asparagus is tender but bright green.

Blanch reserved asparagus tips in boiling water for 2 minutes, then plunge into ice bath. Set aside.

Remove pot from heat and use an immersion blender to puree the mixture until smooth. Stir in heavy cream and lemon juice, season with salt and pepper. Let cool to room temperature, then refrigerate for at least 4 hours or overnight.

Serve in chilled bowls, garnished with blanched asparagus tips, chopped chives, and a drizzle of olive oil.