- Slice kernels off corn cobs (you should have 3 to 3 1/2 cups kernels). Discard cobs and place kernels in a blender.
- Add buttermilk, basil, scallions, lime juice, garlic, salt and 1/3 cup ice cubes to the blender and purée until very smooth.
- Strain mixture through a sieve, pressing down hard on the solids.
- Serve soup garnished with radish slices and a drizzle of olive oil.