Wrap the tenderloin in plastic wrap and place in the freezer for 2 hours.
After 2 hours, unwrap the tenderloin and thinly slice the beef into approximately into 1/8 to 1/4-inch pieces. Lay out sheets of plastic wrap and place each slice onto the plastic. Top with another piece of plastic and gently pound the meat with a meat mallet until paper-thin. Repeat until all of the meat is sliced and pounded. Divide the meat evenly among 4 chilled plates.
Quick Tip: To shave Parmesan, I always go to a simple vegetable peeler - never a knife. Just slide your peeler across one side of your Parmesan block to get beautiful shaved pieces of cheese.
Serve with arugula that has been tossed with olive oil, lemon juice, salt, and pepper. Top with shaved Parmesan.