Wrap each ear of corn with a 2-inch band of foil to keep husks in place. Soak corn in a large bowl of cold water, 10 minutes. Remove from water, shaking off excess. Grill corn directly over heat source, turning often, until husks are charred and kernels are tender, 8 to 10 minutes.
Transfer corn to a platter. Peel back husks and spread sour cream over cobs with a butter knife. Sprinkle evenly with cheese and paprika. Season to taste with salt and pepper and serve immediately.