You don't have to spend an arm and a leg at a deli to enjoy this classic sandwich.
In a small bowl, combine mayonnaise, ketchup, and relish; season with salt and pepper. Set aside. Butter bread; place, buttered side down, on a work surface. Spread 4 slices with mayonnaise mixture; top with corned beef, sauerkraut, and cheese. Sandwich with remaining bread, buttered side up.
In 2 batches, cook sandwiches, covered, in a large skillet over medium-low, until bread is golden brown and cheese is melted, 2 to 3 minutes per side.