Wrap the beef tenderloin tightly with plastic wrap and place in the freezer for 1 hour.
Meanwhile, add all the vinaigrette ingredients to a sealable Mason jar. Seal the jar and shake vigorously. Set aside.
Using a sharp knife, cut the beef tenderloin into thin slices and place on a large serving dish. Garnish with arugula, toasted hazelnuts, Parmesan cheese petals and capers. Drizzle some of the vinaigrette over the carpaccio and season with sea salt and ground pepper. Serve immediately, with the remaining vinaigrette on the side.