Place tenderloin into the freezer for about 15 minutes, until it is firm and slightly frozen. It will be easier to slice when it’s partially frozen.
Toss arugula and red onion with the juice of one lemon half and ¼ cup of olive oil. Season with salt and pepper.
Arrange 4 plates on the counter top. Slice the beef with a sharp knife into very thin slices, laying them directly onto each plate as they are sliced, overlapping slightly and working in the centre of the plate. Drizzle each serving with 1 tbsp of the olive oil and garnish with a handful of the dressed arugula, pecorino shavings and salt and cracked black pepper. Serve immediately.