Boil corn in salted water, covered, 2 to 3 minutes. (For a smoky flavor, you can also roast or grill the ears instead of boiling them.) Slice kernels off the ears with a sharp paring knife. In two batches, purée kernels in a blender with 4 cups water. Strain purée into a bowl, pressing to squeeze out the corn liquid, and throw away the kernel mash. Add salt to taste and chill soup until cold, at least 3 hours. Meanwhile, boil tightly packed fresh basil leaves for 2 to 3 seconds. Drain immediately, plunge in ice water, and drain again. Purée basil in a blender with 1/2 teaspoon salt and the olive oil. Serve soup cold, drizzled with basil oil.