In a bowl, combine the EVOO, garlic, chives and sage. Season the steaks with salt and pepper, then coat with the oil mixture.
Heat a large skillet over high heat. Add 2 steaks and cook for 5 minutes on each side for medium-rare or 8 minutes for medium. Transfer to a plate. Wipe the skillet clean and repeat with the remaining steaks. Top the steaks with the cheese, tent with foil and let stand for 5 minutes.
Toss the arugula and tomatoes with the lemon juice, a drizzle of EVOO, and salt and pepper to taste. Serve alongside the steaks and pass the bread around the table.