Clean and wash the radishes and cut into small pieces. Cut the cress from the bed and place in a colander. Rinse off briefly with cold water, drain well and put some of it aside for decoration.
Put the radishes with cress, horseradish and lemon juice in the blender and puree finely. Add the buttermilk and mineral water and mix everything again.
Season the radish milk with salt and pepper, fill into glasses and garnish with the cress. Serve with a straw if desired.