Prepare the asparagus – Trim the woody ends from the asparagus and chop into small pieces.
Sauté the aromatics – In a medium saucepan, melt the butter over medium heat. Add the shallot and garlic, cooking until soft and fragrant, about 2 minutes.
Simmer the soup – Add the chopped asparagus and vegetable broth. Bring to a gentle simmer and cook for 10-12 minutes, until the asparagus is tender.
Blend until smooth – Using an immersion blender (or transferring carefully to a regular blender), purée the soup until smooth.
Finish with cream and seasoning – Stir in the heavy cream, lemon juice, salt, and white pepper. Simmer for another 2 minutes, then remove from heat.
Soft-boil the eggs – While the soup is cooking, bring a small pot of water to a gentle boil. Carefully add the eggs and cook for 6 minutes. Transfer to an ice bath, then peel and halve.
Serve – Ladle the soup into bowls, top with the halved soft-boiled eggs, and sprinkle with fresh chives. Serve alongside rye crackers.