Prepare a charcoal grill with hot coals or turn a gas grill to medium-high heat.

Meanwhile, pat dry the filets mignons with paper towels. Brush the filets lightly all over with the oil. Combine the fleur de sel and cracked pepper on a plate and roll the filets on all sides in the mixture, pressing lightly to help the salt and pepper adhere. The steaks should be evenly coated with the fleur de sel and cracked pepper.

Meanwhile, whisk together the olive oil, lemon juice, mustard, kosher salt, and freshly ground black pepper. Set aside.

When the grill is ready, place the steaks on the grill. Cook them for 5 minutes on each side for medium-rare or until the centers of the steaks register 125 degrees on an instant-read -thermometer. Remove to a plate, cover tightly with foil, and allow to rest for 10 minutes before slicing thickly.

Toss the arugula in a large bowl with enough of the dressing to moisten; divide among 4 plates. Place a steak on top of each salad. Shave the Parmesan onto each steak with a vegetable peeler, sprinkle with salt, and serve hot.