Heat a large soup pot over medium heat, then add the butter and leeks. Sauté for 5 minutes. Add the apple cider vinegar, and stir to scrape the browned bits from the bottom of the pot.
Add the potato, broth, salt, and pepper, and bring to a boil. Reduce the heat to a simmer, and cook uncovered for 5 minutes (or until the potatoes are tender). Add the asparagus and cook for 5 minutes more (or until the asparagus is tender).
Remove the pot from the heat and add the cream.
Blend in small batches until smooth. Then, to ensure a silky smooth texture, run the blended soup through a fine mesh sieve and discard any pulp.
Transfer the soup to a bowl and chill for 2 hours. Taste and add more salt if desired.
Serve chilled with a drizzle of cream, chives, and a twist of black pepper.