Preheat a grill or grill pan to high. Pulse the olives, shallot, garlic, rosemary, red pepper flakes, 2 tablespoons olive oil and the juice of 1/2 lemon in a food processor; season with salt and pepper.
Pierce the steak all over with a fork and season with salt and pepper. Rub 1 heaping tablespoon olive mixture all over the steak, then set aside, about 10 minutes. Meanwhile, toss the remaining olive mixture with the tomatoes, parsley, the remaining 2 tablespoons olive oil and the juice of the remaining 1/2 lemon in a small bowl.
Grill the steak until browned on one side, about 7 minutes. Flip and cook about 7 more minutes for medium rare.
Transfer the steak to a cutting board and let rest 5 minutes.
Cut in half; reserve one half for steak sandwiches (at right). Thinly slice the remaining steak against the grain and top with the olive-tomato tapenade.
