Coat the steak with 1 tablespoon of the salt and set on a rack inside a rimmed pan and leave at room temperature for 30 minutes. The steak should come up to somewhere between 45 and 50°F. Tear off an 18-inch long piece of heavy-duty aluminum foil and have it standing by near the cooktop
When about 5 minutes of the salting time remains, place a 12-inch cast iron skillet over the highest heat you’ve got for a full 5 minutes. You will want to crank up your ventilation hood to high and open a window; there’s gonna be smoke.
Evenly sprinkle the remaining tablespoon of salt across the bottom of the hot skillet. Lightly coat both sides of the steak with the oil. Place right in the middle of the pan and don’t touch it for 2 minutes. Flip and rotate 90 degrees so that the steak hits fresh pan (and fresh salt) and cook another 2 minutes, uninterrupted.
Turn the steak up on one long edge and cook for 30 seconds, then turn and cook along the opposite edge for another 30. If you’re checking, its internal temperature should be between 70° and 72°F. Transfer to the foil and wrap tightly for 3 minutes. During this time leave the skillet on the heat. (Did I mention there would be smoke?)
After 3 minutes, unwrap the steak and place it back in the pan for 3 minutes, then flip and cook for another 3. Flip and cook another 2, then flip and cook a final 2 minutes. At this point, the internal temperature should be 120°F. (If you prefer your steak more on the rare side, decrease the final cook times to 2 minutes, 2 minutes, then 1 and 1. Its internal temperature should be between 105 and 110°F.)
Return the steak to the foil and wrap tightly to rest for 5 minutes. Then unwrap and slice thin on the bias. Serve with any accumulated juices.