Start marinating the meat up to a day in advance to allow the flavors to blend.
- Trim fat from steaks. Season steaks with kosher salt and black pepper. Place in a large self-sealing plastic bag and set in a shallow dish.
- For marinade, in a small bowl, combine 2 tablespoons of the olive oil, 1 tablespoon of the mint, the rosemary, and crushed red pepper. Pour over steaks. Seal bag; turn to coat steaks. Marinate in the refrigerator for 1 to 24 hours, turning bag occasionally.
- For dressing, in a screw-top jar, combine lemon juice, red wine vinegar, and remaining 2 tablespoons olive oil. Cover and shake well. Season to taste with additional kosher salt and black pepper. Set aside.
- Drain steaks, discarding marinade. For a charcoal grill, place steaks on the rack of an uncovered grill directly over medium coals. Grill for 14 to 18 minutes for medium-rare doneness (145°F) or 18 to 22 minutes for medium doneness (160°F), turning once halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Place steaks on grill rack over heat. Cover and grill as above.)
- Remove steaks from grill. Cover with foil and let stand for 5 to 10 minutes. Slice meat across the grain.
- In a large bowl combine arugula, celery, tomatoes, and the remaining 1 tablespoon mint. Drizzle with the dressing; toss to coat.
- To serve, divide arugula mixture among four dinner plates; top with meat slices. Sprinkle with Parmesan cheese.