Tightly wrap the beef in plastic wrap and place it in the freezer for about an hour until it's slightly firm.
While the beef is chilling, prepare the sauce by mixing mayonnaise, 2 tablespoons of lemon juice, anchovies, and 1/4 teaspoon of pepper in a food processor. Blend until you achieve a smooth consistency and set aside.
Once the beef is ready, unwrap it and, using a sharp knife, slice it into extremely thin pieces.
Arrange the thin slices of beef evenly on 4 pre-chilled plates.
In a bowl, toss arugula with the remaining lemon juice, olive oil, salt, and pepper.
Place the arugula mixture in the center of the beef slices, drizzle with the prepared sauce, and top with capers and cheese.