Season both sides of the steaks with the olive oil, salt and pepper.
Heat a large skillet over medium-high heat.
Add the butter to the skillet once hot to melt.
Place the steaks in the skillet and cook for about 4 minutes on one side until nicely browned.
Flip steaks, top each with two slices of cheese, cover the skillet and let cook another 3 minutes until cheese is melted.
Transfer steaks to a plate and let sit.
Spoon the sauerkraut onto the skillet (in the steak grease) in two flattened piles. Continue cooking over medium high heat for about 5 minutes until golden brown and starting to crisp on the edges.
While that cooks, make the sauce by combining the yogurt, lemon juice, mayonnaise, ketchup, pickle and horseradish in a small bowl. Season with salt and pepper to taste.
Transfer each pile of the sauerkraut to the top of the steaks.