01 - Preheat oven to 375°F. Line a baking sheet with parchment paper.
02 - In a small bowl, combine melted butter, minced garlic, chopped parsley, sea salt, and Parmesan cheese. Stir until evenly blended.
03 - Slice slider buns in half. Brush 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. Set aside.
05 - Pat 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 filet medallions for 2 to 3 minutes per side for medium-rare, adjusting time for preferred doneness. Transfer to a plate and 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 with the top bun.
08 - Serve immediately while warm.