This exquisite dish is the perfect appetizer for your next social gathering.
Rub the beef with olive oil and sprinkle all over with 2 teaspoons kosher salt and 1 teaspoon freshly ground black pepper. Heat a saute pan over high heat and sear the filet on all sides, turning it with tongs. Wrap the beef in plastic wrap and freeze for 2 hours, turning once to freeze evenly.
Meanwhile, place the egg yolks, mustard, garlic, anchovies, lemon juice, 2 1/2 teaspoons kosher salt, and 1 teaspoon pepper in a food processor fitted with the steel blade and process for 15 seconds. Combine the 3/4 cup olive oil and the canola oil in a glass measuring cup. With the food processor running, slowly pour the oils down the feed tube in a thin stream. Add the grated Parmesan and pulse to combine.
Remove the string from the beef and slice it very thin with a sharp slicing or smoked salmon knife. Place 5 slices on each dinner plate in a single layer. Drizzle the beef generously with the dressing and (in this order) sprinkle with the capers, kosher salt, pepper, arugula, shaved.
Parmesan, and sea salt. Serve at room temperature with a pitcher of extra dressing on the side.