An hour before grilling, take your steaks out of the fridge and sprinkle generously with salt and pepper. Leave on the counter while you light your fire/heat your grill.
Place the arugula on a large platter and drizzle with 2 tbsp of the olive oil and some lemon juice.
If using a wood fired oven, grill steaks for 3 minutes per side using a grill attachment. Do not place the steaks directly over the flame, but just a little off to the side. You do want your oven to be quite hot - about 500 degrees.
Place steaks immediately on top of your prepared arugula and drizzle steaks with remaining olive oil. Scatter Parmesan on top of each steak and finish with an extra sprinkle of sea salt and pepper. Let steaks rest like this for 10 minutes before serving.
You may also prepare this dish on a charcoal barbecue. You will want to increase the cooking time if you choose that route --- about six minutes per side for medium doneness.