Preparation

• Heat a gas grill to medium or prepare a medium-hot charcoal fire. Drizzle the steak with 1 Tbs. of the oil and season it all over with 1-1/4 tsp. salt and 1/2 tsp. pepper.
• Lightly oil the grill grates. Grill the steak, flipping once, until nicely browned on each side and cooked to your liking (16 to 17 minutes total for rare; 19 to 20 minutes total for medium-rare; 22 to 24 minutes total for medium). Transfer the steak to a large platter or cutting board, cover loosely with foil, and let rest for 10 minutes before carving.
• Meanwhile, in a large bowl, whisk together the remaining 3 Tbs. oil with the lemon juice. Season to taste with salt and pepper. Add the arugula to the bowl and toss gently to coat with the dressing. Check for seasoning and adjust if necessary. Garnish the salad with the Parmigiano.
• Sprinkle the steak with a pinch of salt. Slice the steak across the grain and divide between 4 dinner plates. Serve the arugula salad on the side.