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Season steak liberally on all sides with salt and pepper. Set on wire rack set in rimmed baking sheet and place in refrigerator uncovered overnight.
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2 Meanwhile, place potatoes in a medium pot, cover with water, season with salt, and bring to a boil over high heat. Reduce to a simmer and cook until tender, about 10 minutes total. Meanwhile, remove leaves from 1 sprig of rosemary and 1 sprig of thyme and finely chop. Set aside. Drain potatoes and set aside to cool. Cut each potato in half lengthwise. Potatoes can be cooked through this stage up to a day in advance and stored in a sealed container in the refrigerator.
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3 Heat oil in a 12-inch heavy-bottomed cast-iron skillet over high heat until just beginning to smoke. Carefully add steak and cook, flipping frequently, until a pale golden brown crust starts to develop, about 4 minutes total.
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4 Reduce heat to medium. Add 3 tablespoons butter, garlic, whole rosemary sprigs, and whole thyme sprigs to the skillet and continue to cook, flipping steak occasionally, and basting any light spots with foaming butter. To baste, tilt pan slightly so that butter collects by handle. Use a spoon to pick up butter and pour it over steak, aiming at light spots. Continue flipping and basting until an instant read thermometer inserted into thickest part of tenderloin side registers 115 to 120u00b0F for medium rare, or 125u00b0F for medium, 6 to 8 minutes total. Immediately transfer steak to a wire rack set in a rimmed baking sheet and place herb sprigs and garlic on top. Allow steak to rest uncovered while you cook the potatoes.
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5
5 Return skillet to medium-high heat and add remaining tablespoon butter. When foaming subsides, add potatoes, cut-side down. Cook, shaking pan occasionally, until potatoes are deep golden brown and crisp, about 8 minutes. Add chopped rosemary and thyme, season with salt and pepper, and toss to coat potatoes. Cook, tossing and stirring, until fragrant, about 1 minute.
