Bring to a boil, reduce the heat, and simmer until the asparagus is tender, 5 minutes. Puree until smooth. Return to the pot and stir in the reserved asparagus tips and:
1/4 to 1/2 cup heavy cream or half-and-half
Salt to taste
1/8 teaspoon ground black pepper
Simmer for 3 to 5 minutes and ladle into warmed bowls. Garnish with:
Chopped fresh parsley, snipped fresh dill, or snipped fresh chives