If beef is thick, slice in half horizontally to make thinner slices.
Prepare the sauce. In a small bowl, mix the mayo and horseradish sauce. Add ground pepper to taste. Refrigerate until needed.
Melt butter in skillet or griddle. Sear steak 2 minutes on each side. Test for doneness; they should be rare/medium rare inside. Remove from heat and let sit for 3-5 minutes.
Open the slider buns and place them cut side down in the same skillet. Toast for 1-2 minutes, watching so they don't burn.
Spread sauce on bottom half of bun. Add the beef, then, if desired, lettuce, tomato and pickle.
*Use the best cut of beef your budget allows. We used top round, but you could also use a filet or tenderloin, adjusting the cook time accordingly.
**We used Martin's Potato Rolls for our slider buns, but you could substitute dinner rolls or ciabatta bread.