a meat thermometer or leave-in digital probe thermometer
Remove the steaks from the fridge 2 hours before cooking to allow them to come up to room temperature.
Heat your oven to 250 degrees F and dry off the outside of the steak with paper towel. Place the steaks on a rack-lined sheet pan and season generously with salt and pepper.
Cook the steak in the low oven until the internal temperature reaches 105 degrees F (40 degrees C) for rare (about 25 minutes) or 115 degrees F (46 degrees C) for medium-rare (about 30 to 35 minutes), being sure to check the temperature often as cooking times can vary depending on the thickness of your steak, its temperature when it went into the oven and your oven’s consistency. For ease, I suggest using a leave-in digital probe thermometer.
Meanwhile, heat a large cast-iron skillet over high heat. Alternatively, heat your grill to high.
When the steaks are up to temperature, remove from the oven and rub the outside with the butter or oil. Transfer to the skillet or grill and sear, flipping frequently, until golden and seared on both sides, 2 to 3 minutes total.
Meanwhile, toss the arugula with the lemon zest, lemon juice and a glug of olive oil and season with salt and pepper.
With this cooking method, you do not need to rest your steaks! Simply remove the steaks from the heat and slice thickly against the grain. Serve topped with shavings of Parmigiano-Reggiano with the lemony arugula on the side.
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