01 - Preheat oven to 375°F. Line a baking sheet with parchment paper and set aside.
02 - In a small bowl, combine the melted butter, minced garlic, chopped parsley, sea salt, and Parmesan cheese. Stir until well blended.
03 - Slice each slider bun 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, or until golden brown 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 shimmering. Sear the filet medallions for 2 to 3 minutes per side for medium-rare, adjusting time to your preferred doneness. Transfer the medallions to a plate and let rest for 5 minutes.
07 - Place a few arugula leaves on each bottom bun. Top with a filet mignon medallion, a slice of Roma tomato, and a few rings of sliced red onion. Drizzle with horseradish cream or aioli if using. Cap each slider with the top bun.
08 - Serve the sliders immediately while warm.