Make the Russian dressing. In a small bowl, whisk mayonnaise, onion, ketchup, horseradish, hot sauce, Worcestershire sauce, paprika, and salt to taste. Set aside.
Warm the buns. Heat your oven to 325°F or 163°C. Once the oven is heated, turn it off. Place the slider buns on a baking sheet in the hot oven.
Bake the sliders. Remove the buns from the oven and turn on the broiler. Split the rolls and top the bottom half with corned beef, sauerkraut and 2 cheese squares per bun. Place the sandwiches under the broiler in the middle oven rack until the cheese melts. Remove from the oven.
Finish assembling. Spread the Russian dressing onto the inside of the bun tops and place onto the sandwiches. Serve.