How to Make It
Heat a medium cast-iron skillet until hot. Lightly rub the steak with olive oil and season generously with salt and pepper. Add the steak to the hot skillet and cook over moderate heat until browned on the bottom, about 6 minutes. Add the garlic cloves, herb sprigs and butter to the skillet. Turn the steak and cook for 5 minutes. Using kitchen tongs, turn the steak on each side and cook until browned, about 2 minutes per side. Lay the steak flat, baste it with the butter in the skillet and turn the garlic cloves. Continue to cook the steak for about 5 minutes longer, until an instant-read thermometer inserted in the center registers 125° for medium-rare. Transfer the steak and garlic cloves to a cutting board and let rest.
Meanwhile, bring a small saucepan of water to a boil. Add all but 1 cup of 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 mini food processor. Add the ice cube, 3 tablespoons of the pine nuts, the Parmesan and the 1/4 cup plus 2 tablespoons of olive oil. Process to a fine paste. Season the pesto with salt and pepper.
Spoon the pesto onto 2 plates. Thinly slice the steak and arrange on the pesto. Mound the remaining 1 cup of arugula on the steak and drizzle with any steak juices. Garnish with the remaining 1 tablespoon of pine nuts and the garlic cloves and serve.