Season one piece of Strip loin with salt and pepper. Heat a large pan with oil and sear on all sides until brown.
Remove to a lined sheet pan and roast in a preheated oven until the internal temperature reads 145° F. Allow to rest and cool.
Using a meat slicer set to the thinnest setting, shave the cooled roast against the grain.
Mix together mayonnaise and drained horseradish.
Spread the inside of the bun with the mayo mix. Layer the sliced cheese, 3 oz of sliced beef, tomatoes and arugula.