Chop 2/3 the cucumber coarsely in chunks. Prepare 1/2 the avocado the same way. In a blender puree together the chopped cucumber, chopped avocado, shallots, mint, buttermilk, lemon juice, water and salt until smooth. Add a bit more water if too thick.
Chop remaining cucumber and avocado into small pieces and add to the soup. Stir well.