Wash asparagus; break off woody bases where spears snap easily. Cut off tips; set aside. Chop remaining asparagus stalks. In a medium saucepan, combine chopped asparagus stalks, vegetable broth, and potatoes. Bring to boiling; reduce heat. Cover and simmer about 5 minutes or just until asparagus is barely tender. Remove from heat. Cool for 5 minutes. Pour into blender. Cover and blend until pureed. Return to saucepan.

Meanwhile, in a small saucepan, combine the water and reserved asparagus tips. Bring to boiling; reduce heat. Simmer, uncovered, for 3 minutes. Drain and set aside. Add soy milk or rice milk to pureed mixture; stir until well mixed. Stir in the chopped basil; heat through. Stir in asparagus tips. Season to taste with salt and pepper. If desired, garnish individual servings with basil leaves. Serve immediately.

Hints: Try making this in a stainless steel pot and process it with an immersion blender directly in the pot. (An immersion blender is a small, hand-held appliance that will blend foods without removing them from the cooking pot or bowl. Do not use an immersion blender in a pot that is not stainless steel.)