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. Mix until evenly blended.
03 - Slice slider buns in half. Brush cut sides generously with the garlic butter mixture and arrange on the 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 - Layer 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. Pairs well with a light red wine such as Pinot Noir.