Preheat your oven to 275 degrees F. Season your steak on both sides with kosher salt and black pepper. You don't need to take the steak out of the fridge in advance.
Line a rimmed baking sheet with foil for easy cleanup. Fit the baking sheet with a metal rack. Grease the rack.
Place the steak on the rack. Insert the probe of a meat thermometer (I got mine on Amazon) into the steak. Bake the steak until it reaches an internal temperature of 110 degrees F. For me, with a fridge-temperature, 1 ½ inch thick steak, this usually takes about 20 minutes.
Remove the steak from the oven. Transfer it to a plate, loosely cover it with foil and allow it to rest for 10 minutes.
While the steak is resting, heat a cast-iron skillet over high heat until smoking hot, 5-7 minutes. If the skillet is well-seasoned, you don't need to grease it.
Gently pat the steak dry with paper towels, then place it in the hot skillet. Sear the steak for 1 minute on each side and a few more seconds on the edges, then top with butter and serve.
The USDA recommends cooking steaks to 145F which is medium.
When it comes to searing, the best tool is a well-seasoned cast-iron skillet. It's superb in terms of heat retention and distribution and cooks steaks perfectly. It's the only type of skillet I use when cooking steaks.
While this recipe was written for New York strip steaks, it also works with other thick cuts, including ribeye and filet mignon.