Place corn cobs in boiling water and cook for 5 minutes.
Slice kernels off cobs.
Discard cobs and place kernels in a blender.
Add buttermilk, basil, scallions, lime juice, garlic and salt, to the blender, and purée until very smooth.
Place in an airtight container and chill for at least 4 hours, or overnight, prior to serving.
Serve soup garnished with cilantro leaves and a drizzle of olive oil.