Working in a large bowl, cut kernels from cobs with a sharp knife and set aside. Scrape back of knife several times against cobs to extract remaining corn pulp, scraping into a large glass measure. (You should have at least 3/4 cup of corn pulp. If not, add 2 tablespoons crème fraîche.) Transfer pulp to a blender and purée with 2 tablespoons crème fraîche until smooth.
Cook shallot in butter in a 12-inch heavy skillet over moderate heat, stirring occasionally, until softened, 3 to 4 minutes. Stir in kernels, then add corn purée, water, salt, and pepper and simmer, uncovered, stirring occasionally, until kernels are just tender, 3 to 4 minutes. Stir in basil to taste.
