1. Cut tips from asparagus. Set aside. Chop remaining stalks into 1/2-inch pieces. Melt butter in a 4-quart saucepan over medium heat. Add onion; cook 3 minutes. Add asparagus stalks and cook an additional 2 minutes. Add broth, potatoes, salt, dill and pepper. Bring to a boil.
2. Reduce heat to medium-high and cook 10 to 12 minutes uncovered, until potatoes are very tender. Meanwhile, place asparagus tips in a small glass bowl with 1 tablespoon water. Cover with plastic wrap and microwave on HIGH for 1 minute.
3. Remove soup from heat and puree until smooth. Stir in heavy cream. Serve warm or chilled, garnished with asparagus tips.