1. Coarsely chop the parsley leaves and the garlic. Transfer to a small bowl, mix with the olive oil, and season with salt and pepper. Rub marinade over the steaks and refrigerate, covered, for at least 30 minutes.Vinaigrette:
2. In a bowl, whisk together lemon zest, lemon juice, vinegar, mustard, and salt and pepper to taste. Add oil, whisking until dressing is emulsified.
3. Turn the grill to medium-high heat and brush the racks with olive oil. Scrape off any excess marinade from steaks, and grill about 6 inches over heat for 3 to 4 minutes on each side for medium-rare. Transfer steak to a cutting board and let stand for 5 minutes. With a sharp knife at a 45-degree angle, cut steaks, across the grain, into 18 thin slices.
4. Toss arugula with dressing to coat. Divide among 6 plates. Top each with steak strips, sprinkle with cheese, and serve.