Wrap the beef in plastic wrap and tighten each end like a sausage so that the beef has a neat shape. Refrigerate for an hour before slicing. Chill the serving plates in the refrigerator too.
Just before slicing the beef, lay out the plates and put a drop or two of olive oil and a little salt on each one; this will give the beef a better depth of flavor and prevent it from sticking.
Trim off all the fat from the beef, then slice the meat as thinly as possible.
Lay four squares of plastic wrap on the work surface. Place an equal amount of sliced beef on each piece of plastic, positioning the slices so they do not overlap. Top with another sheet of plastic wrap, and press down to seal.
Using a rolling pin, gently tap the beef so that it spreads out and becomes wafer-thin and, if possible, about the same size as the plate you are going to serve it on.
Remove the top layer of plastic wrap and invert the carpaccio onto a plate. Peel off the other piece of wrap. Drizzle with a little olive oil, and use your fingers to spread the oil all over the meat (This prevents it from changing color and drying out).
In a bowl, dress the arugula with 2 tsp. of olive oil, some pepper, and a few flakes of sea salt, mixing well. Add a little lemon juice to taste (it needs to be sharp but not enough to make you screw your eyes up). Scatter the dressed arugula over the plates of carpaccio, followed by the Parmigiano shavings. Drizzle with the truffle oil. Grind some more pepper over and serve each plate with a wedge of lemon.