01 - Preheat oven to 375°F. Line a baking sheet with parchment paper.
02 - In a small bowl, combine the melted butter, minced garlic, chopped parsley, sea salt, and Parmesan cheese. Mix until well blended.
03 - Slice the slider buns in half. Brush the cut sides generously with the garlic butter mixture and arrange on the prepared baking sheet, cut side up. Sprinkle with additional Parmesan if desired.
04 - Bake the buns for 7 to 9 minutes until golden and fragrant. Remove from the oven and set aside.
05 - Pat the filet mignon medallions dry with paper towels. Season each side evenly with kosher salt and freshly ground black pepper.
06 - Heat olive oil in a heavy skillet or cast iron pan over medium-high heat until the oil just begins to shimmer. Sear the medallions for 2 to 3 minutes per side for medium-rare, adjusting the time to your preferred doneness. Transfer to a plate and let rest for 5 minutes.
07 - Layer a few arugula leaves on each bottom bun. Place a filet mignon medallion on top, followed by a slice of Roma tomato and a few rings of sliced red onion. Drizzle with horseradish cream or aioli if using. Cap with the top bun.
08 - Serve the sliders immediately while warm.