Line a baking sheet with parchment paper. While the cornflakes are still in the bag, smash them with a pan or measuring cup until they are the consistency of breadcrumbs. Set up a breading station: put the flour in one bowl and season with the salt and pepper; put the eggs in another. Put the bag of cereal crumbs on the side.
Cut the string cheese in half crosswise so they are the length of regular mozzarella sticks. Dip each piece in the flour to coat, shake off the excess, drop in the eggs and then drop in the bag of cornflake crumbs and shake to coat. Drop the coated cheese back in the egg and then cover with another layer of cornflakes. Place on the prepared baking sheet. Bake the sticks until the cheese melts, 5 to 7 minutes.