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1
Heat a medium cast-iron skillet until hot.
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2
Lightly rub the steak with olive oil and season generously with salt and pepper.
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3
Add the steak to the hot skillet and cook over moderate heat until browned on the bottom, about 6 minutes.
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4
Add the garlic cloves, herb sprigs and butter to the skillet.
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5
Turn the steak and cook for 5 minutes.
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6
Using kitchen tongs, turn the steak on each side and cook until browned, about 2 minutes per side.
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7
Lay the steak flat, baste it with the butter in the skillet and turn the garlic cloves.
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8
Continue to cook the steak for about 5 minutes longer, until an instant-read thermometer inserted in the center registers 125 for medium-rare.
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9
Transfer the steak and garlic cloves to a cutting board and let rest.
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10
Meanwhile, bring a small saucepan of water to a boil.
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11
Add all but 1 cup of the arugula and cook for 10 seconds, then drain and cool under running water.
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12
Squeeze out the excess water and transfer the blanched arugula to a mini food processor.
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13
Add the ice cube, 3 tablespoons of the pine nuts, the Parmesan and the 1/4 cup plus 2 tablespoons of olive oil.
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14
Process to a fine paste.
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15
Season the pesto with salt and pepper.
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16
Spoon the pesto onto 2 plates.
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17
Thinly slice the steak and arrange on the pesto.
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18
Mound the remaining 1 cup of arugula on the steak and drizzle with any steak juices.
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19
Garnish with the remaining 1 tablespoon of pine nuts and the garlic cloves and serve.
