Heat the oil in a pan. Briefly sauté the shallot and garlic, add the asparagus, cook briefly. Pour in the water, bring to the boil, season. Cover and cook for approx. 25 mins. until soft, add the bread, radish and yoghurt, puree until smooth, leave to cool completely. Cover the soup and chill for at least 2 hrs.
Heat the oil in a frying pan. Fry the reserved asparagus tips for approx. 5 mins. Remove, combine with the radish, radish greens, balsamic and oil, season. Garnish the soup with the topping.