Season the beef with the salt and pepper. Heat a skillet over medium-high heat and add the olive oil. Once it’s hot, add the filet and cover the skillet. Sear the filet on both sides until it’s golden brown and cooked to your desired doneness. I like mine cooked medium, and that takes 2 to 3 minutes of searing when the skillet is covered. Once the beef is cooked, place it on a cutting board and let it rest for 10 minutes. Slice it into 1/4-inch thick pieces.
Rub a fondue pot with the garlic clove. Chop the clove in half and mince it. Add a sprinkle of salt to the garlic and mash it with a fork and knife to create a paste.
In a small saucepan, bring the wine to a simmer over medium heat. Toss all of the grated cheese with cornstarch. Add the cheese to wine in batches, stirring constantly until smooth. Add the garlic paste and nutmeg and stir. Pour the fondue into a fondue pot (preferably one that is heated underneath) – use the fondue for dipping the sliders, or simply use it as a cheese sauce op top the sliders.
Add the arugula to a bowl and toss it with a drop of olive oil and a pinch of salt and pepper. To assemble the sliders, toast the buns if desired. Add slices of the filet topped with the fondue and arugula.