I was recently assigned an article on Minnesota hotdish, and never encountered radish soup during my research. Asian style, soups and stews with daikon radish is routine for me. I had stored away in my head how I might cook and marry little red radishes with radicchio, but have yet to try anything. I can't yet seem to acquire a taste for cooking other Asian veggies like cucumber and lettuce, but continue to occasionally try.
This is admittedly a tame idea, but it's good. Finely grate a tablespoon of raw radish. Finish a soup serving with a dollop. It gives the soup a refreshing little peppery bite.