Butter one side of each slice of bread. On the non-butter side spread Russian dressing on each slice. Top half of the slices with cheese, corned beef, and sauerkraut. Top each sandwich with remaining slices, dressing side down. Heat a medium skillet over medium heat. Place a sandwich in skillet and cook until golden and cheese is melted, 3 minutes per side.
In a medium bowl, whisk together mayonnaise, ketchup, horseradish, Worcestershire, sugar, and paprika until combined. Season with salt and pepper.