Refrigerate.

Prepare an ice-water bath and set aside. In a large saucepan, bring 4 cups salted water to boil. Add asparagus tips and boil about 3 minutes, then place in ice bath until cooled. Drain tips and lay to dry on a paper towel.

In a large saucepan, melt butter and cook leeks, stirring well, until softened, about 5 minutes. Add potatoes, stock, and white wine, and bring to a boil. Reduce heat to low and simmer 15 minutes or until potatoes are tender. Add remaining asparagus (not reserved tips) and cook over medium heat 8 to 10 minutes. Remove from heat and puree (be cautious of the hot liquid). Allow soup to cool to room temperature, then strain through a sieve and discard solids. Stir in heavy cream and season with salt and pepper to taste. Refrigerate at least 3 hours or overnight.

To serve, place about 2 tablespoons crabmeat mixture into each of 10 chilled soup bowls and ladle soup on top. Garnish with a small dollop of crabmeat mixture and reserved asparagus tips.