Make the Russian dressing. In a small bowl, whisk together mayonnaise, sour cream, ketchup, horseradish, paprika, and a pinch of salt. Set aside.

Warm the corned beef. If the corned beef is cold, warm it in a skillet with 1/4 cup broth or water over medium heat. Simmer gently until heated through, then drain any excess liquid.

Toast the bread. In a large skillet over medium-low heat, melt 2 tablespoons of butter. Add 4 slices of rye bread and toast one side until golden brown. Keep an eye on the bread to prevent burning.

Transfer the toasted bread to a plate, toasted side down. Spread a layer of Russian dressing on the bread, then add corned beef, sauerkraut and 1-2 slices of Swiss cheese. Top with the slice of untoasted bread.

Add the remaining 2 tablespoons of butter to the skillet. Place the sandwiches in the pan with the untoasted bread facing down. Gently press down on each sandwich with a spatula. Cover the skillet with a lid and cook on medium-low heat until the bread is golden and the cheese is melted, about 5-8 minutes.

Cut each sandwich in half and serve warm.