Freeze the beef tenderloin for around 1 hour until it is firm. Using a sharp knife, cut the beef very thinly across the grain. If the slices are thin enough then divide between two plates. If not, then place on a slices on a piece of cling wrap/film, cover with another piece and then flatten with the smooth side of a tenderizer. Transfer to the two plates.
Put the arugula in a bowl. Whisk or shake together the vinaigrette ingredients (truffle oil, EVOO, lemon juice and white wine vinegar, plus sugar and Dijon if using). Pour around half over the arugula and toss.
Divide the arugula between the two plates then top the arugula and the beef with shavings of parmesan. Drizzle over a little more of the vinaigrette and serve.