Make the Dressing – In a medium bowl, whisk together mayonnaise, ketchup, onion, horseradish, pickled relish (if using), Worcestershire sauce, hot sauce (if using), paprika, salt, and black pepper. Cover and refrigerate until ready to use.
Warm the Sauerkraut – Drain the sauerkraut well, then gently press it between paper towels to remove excess moisture. Heat 1 tablespoon vegetable oil in a large skillet over medium heat. Add the sauerkraut and cook, stirring occasionally, until just warmed through, about 1 minute. Transfer to a bowl. Wipe the pan clean.
Warm the Corned Beef – In the same pan used to cook the sauerkraut, heat the remaining 1 tablespoon oil over medium heat. Add the sliced corned beef, separating the pieces with tongs. Cook until warmed through but not browned, about 1 to 2 minutes. Transfer to a plate.
Assemble the Sandwich – Spread softened butter on one side of each rye bread slice. Place the slices on your work surface, buttered side down.On the unbuttered side, spread a generous layer of Russian dressing. Top each with one slice of Swiss cheese, followed by warmed corned beef and sauerkraut. Add a second slice of Swiss cheese on top.Spread Russian dressing on the unbuttered side of the remaining bread slices, then place them on top of each sandwich, dressing side down and buttered side facing up. Repeat with the remaining ingredients to make 4 sandwiches total.
Toast the Sandwich – Heat the skillet over medium-low heat. Place the sandwiches in the pan, cover and cook, until the bottom is golden brown and crisp, about 2 minutes. Flip, cover, and cook the other side until golden, and the cheese is fully melted, another 2 to 3 minutes. Adjust the heat as needed to prevent burning while allowing the cheese to melt.
To Serve – Transfer the reuben sandwich to a cutting board. Slice in half and serve immediately while warm and melty.
Notes
Warming the Sauerkraut and Corned Beef: Heat the ingredients in the microwave in 15- to 30-second intervals until warm. Alternatively, keep them cold if preferred.
Butter Swap: Spread mayonnaise instead of butter on the bread for a crispy sandwich.
For a Sweeter Dressing: Add sugar, honey, or maple syrup.
For a Tangier Dressing: Add lemon juice or vinegar.
For a Spicier Dressing: Use ketchup-style chili sauce, add chili garlic sauce, or increase hot sauce, adjusting levels to taste.