Preheat a large skillet over medium heat. Brush butter on one side of each slice of bread and place buttered-side down onto the skillet until toasted.
Place the bread, buttered-side down on a work surface. Top each slice of bread with a slice of cheese. Then place 2 to 3 slices of the corned beef on half of the slices of bread. Place 2 tablespoons sauerkraut over the corned beef and spoon 1 tablespoon Kicked-Up Russian Dressing onto the remaining slices of bread. Place each of the slices of bread with dressing, buttered-side out on top of the slices of bread topped with corned beef.
Place the sandwiches in the skillet and cook until golden and toasted, about 5 minutes, using a spatula to press down a few times. Turn the sandwiches over and top with foil, then place another pan or skillet on top to press down. Cook until the sandwiches are toasted and the cheese melts, 3 to 5 minutes. Serve with pickles on the side.
In a medium bowl, use a whisk to combine the mayonnaise, chili sauce, horseradish and relish.