Heat the BBQ until hot; lower to medium heat. Lightly rub the steak with olive oil and season generously with salt and pepper. Add the steak to the grill and cook over moderate heat until browned on the first side, about 4 minutes. Add the garlic cloves, herb sprigs and butter.
Turn the steak to the other side for 4 minutes. Using tongs, turn the steak on each of it's sides until browned, about 2 minutes per side. Lay the steak flat, baste with the garlic butter. Continue to cook the steak for about 3 minutes, until an instant-read thermometer inserted in the center registers 125° for medium-rare. Transfer the steak to a cutting board and let rest.
Meanwhile, bring a saucepan of water to a boil. Add the arugula and cook for 10 seconds, then drain and cool under running water. Squeeze out the excess water and transfer the blanched arugula to a food processor. Add all but 2 tablespoons of the pine nuts, the Parmesan and the olive oil. Pulse to a coarse paste. Season the pesto with salt and pepper.
Thinly slice the steak and arrange on a platter. Spoon the pesto over the steak, sprinkle with the remaining pine nuts and serve.
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