Chop the asparagus. Set aside 2 cups of the asparagus tips.
Melt the butter in a stockpot over medium heat. Cook the asparagus, onion, celery, and garlic in the melted butter until beginning to soften, 2 to 3 minutes.
Add the sherry and chicken stock; bring the mixture to a gentle boil, reduce heat to medium-low, and simmer for 45 minutes.
Remove from heat and allow to cool at least 30 minutes.
Pour the soup into a blender, filling the pitcher no more than halfway. Hold the lid in place with a folded kitchen towel and carefully start the blender, using a few quick pulses to get the soup moving before leaving it on to puree. Return the blended soup to the stockpot; stir in the reserved asparagus tips and the heavy cream. Cook over medium heat until soup is hot and the asparagus tips are heated through but still crunchy, about 3 minutes. Season with salt and pepper.