Heat a well-seasoned cast-iron skillet over high heat until smoking hot, 5-7 minutes.
Meanwhile, sprinkle both sides of the steak with kosher salt and black pepper.
Place the steak in the hot skillet. Cook, without moving, for 2 minutes on each side. This will create a nice crust. Cook the fat strip for 30 more seconds.
Using oven mitts, transfer the skillet to the hot oven. Roast the steak to medium rare, 3-4 minutes. For medium, roast for 4-5 minutes.
Place the steak on a plate. Loosely cover it with foil. Allow it to rest for 5 minutes, then top it with butter and serve.
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Notes
Steak Temperature
There's no need to bring the steak to room temperature before cooking it. A cold center allows you to sear the steak well, creating a beautiful crust while keeping it medium-rare. However, I don't recommend cooking from frozen. It's best to thaw the steak in the fridge overnight before cooking it.The CDC recommends cooking meat thoroughly.
What Skillet to Use
If you don't have a cast-iron skillet, carbon steel and stainless steel skillets are good options, though not as good as cast-iron. If you don't have those, use what you have, but adjust your expectations - you will only get a good sear on the steak with the right tool. Don't use a nonstick pan - you can't get those hot enough to sear a steak.If you're not using a pre-seasoned cast-iron skillet, add a tablespoon of avocado oil or clarified butter to the skillet to help prevent sticking. Heat the oil over medium-high heat until shimmering - for about 3 minutes - before adding the steak.To finish it in the oven, if the skillet isn't oven-proof, you'll need to carefully transfer the steak to a rimmed baking sheet that can handle a temperature of 500°F (or preheat the oven to 450°F). Place the baking sheet in the oven to preheat so that when you put the steak on it, it's not cold.If you like steaks and cook them often, I highly recommend getting a pre-seasoned cast-iron skillet like this for $20. It's excellent for many recipes, not just steaks.
Storing Leftovers
Steak is best when served freshly cooked, but you can keep the leftovers in the fridge, in an airtight container, for 3-4 days. Instead of reheating them and risking overcooked meat, I like to slice the leftovers and add them to a salad. But you can also reheat the leftovers gently, covered, in the microwave at 50% power.