Season the steaks (there should be 2 steaks approximately 1 Lb each) with the salt and pepper well in advance of cooking them. At least 2 hours up to 24 hours if possible.
Remove the steaks from the refrigerator 1 hour before cooking to allow to come to room temperature.
Preheat your grill on high heat.
When the grill is hot, add the steaks to the grill. Rotate 90 degrees after approximately 2 minutes.
Flip the steaks and rotate again after 2 minutes. If your grill is very hot, you will have a steak cooked to "Rare Plus" after approximately 8 minutes on the grill.
Remove the steaks from the grill and allow to rest.
While the steaks are resting, shave the parmesan with a microplane.
Place the steak on a bed of arugula.
Spoon 1-2 tablespoons of the vinaigrette onto each steak. Sprinkle half of the grated parmesan cheese on each steak.
Slice each steak and serve family style. Keep the vinaigrette and any extra parmesan at the table.