Melt butter in a large saucepan over medium heat. Stir in the onion, and saute until tender. Mix in the potatoes and radish greens, coating them with the butter. Pour in chicken broth. Bring the mixture to a boil. Reduce heat, and simmer 30 minutes.
Allow the soup mixture to cool slightly, and transfer to a blender. Blend until smooth.
Return the mixture to the saucepan. Mix in the heavy cream. Cook and stir until well blended. Serve with radish slices.
Member Notes: I added garlic, white pepper, and radishes to be blended with the soup. I also have an immersion blender, so I was able to blend the soup without waiting for it to cool and transferring it.