Cut the vein end of the striploin off reserving the remainder of the striploin for steaks. Trim 100% of the fat or sinew off the outside of the striploin. Season generously with salt and pepper. Get a cast iron skillet very hot. Add oil and sear the striploin on all sides creating a nice brown crust. Be sure to only sear the outside. Keep the inside rare/raw. Ensuring the striploin is very cold before searing will help. Once done, place the loin in the freezer. Do not freeze solid, but chill long enough for the beef to become very firm. Then, using a meat slicer, shave the carpaccio as thin as you can while still getting whole pieces.
Mix the mayonnaise, lemon juice and Dijon mustard together for the dressing. Drain and coarsely chop the capers.
Build the sliders by dressing the buns with Dijon dressing and chopped capers. Then add the shaved carpaccio, Parmesan and arugula. Skewer with bamboo pick or skewer if desired. Serve on a platter for sharing.