Place the cornflakes in a zip-top bag and gently crush them with a rolling pin until they resemble coarse crumbs, similar in texture to panko. Pour the crumbs into a shallow bowl or pie plate. In a second shallow bowl or pie plate, whisk together the flour, egg, milk, and salt until smooth. Set both bowls aside.

Spread 1/2 tablespoon of mayonnaise onto one side of each slice of bread. Place 2 slices of bread, mayonnaise side up, on your work surface. Lay two slices of cheese on top of each, then close with the remaining slices of bread, mayonnaise side down, to form sandwiches.

Using a serrated bread knife, trim the crusts from all four sides of each sandwich to create clean, straight edges. Cut each sandwich in half diagonally to make triangular wedges.

Working one wedge at a time, dip each side into the flour batter, making sure it’s fully coated. Let any excess batter drip off, then press all sides into the crushed cornflakes, coating thoroughly. Use your hands to gently press in more crumbs as needed for even coverage. Transfer each wedge to a plate and repeat with the remaining pieces. Place the coated sandwiches in the refrigerator to chill while you heat the oil, for at least 20 minutes or up to 1 day. Chilling helps the sandwiches hold their shape during frying.

While the sandwiches rest, line a large plate with paper towels or set a wire rack inside a baking sheet and set aside. In a large Dutch oven or 10-inch cast iron skillet, pour in oil until it reaches a depth of 1 inch. Heat the oil over medium heat until it reaches 350°F.

Using tongs or a spider skimmer, carefully lower two sandwich wedges into the hot oil. Fry, adjusting the heat as needed to maintain an oil temperature between 330°F and 350°F, until the bottoms are a deep golden brown, about 30 seconds to 1 minute. Flip and cook the other side until golden brown, for another 30 seconds to 1 minute more. Transfer the cooked wedges to the prepared plate or baking sheet. Repeat with the remaining sandwiches. Let cool for 10 minutes before serving.