Preheat the oven to 500°F (260°C), ensuring it reaches full temperature before cooking.
Place a well-seasoned cast-iron skillet over high heat and allow it to heat thoroughly for 5-7 minutes until it begins to emit a faint wisp of smoke. The pan must be scorching hot to create the perfect sear.
As the skillet heats, season both sides of the steak generously with kosher salt and freshly ground black pepper, pressing the seasoning gently into the meat for better adherence.
Carefully lay the steak into the hot skillet, allowing it to sear undisturbed for 2 minutes per side. This step develops a deep, golden-brown crust that locks in flavor. Hold the steak upright with tongs and sear the strip of fat along the edge for an additional 30 seconds, rendering it crisp and flavorful.
Using oven mitts, transfer the skillet directly into the preheated oven. Roast for 3-4 minutes for a perfect medium-rare doneness (135°F), or 4-5 minutes for a classic medium steak (145°F). Check the internal temperature with an instant-read thermometer to ensure precise doneness. If needed, continue roasting in short intervals until the steak reaches the desired temperature.
Once cooked, transfer the steak onto a plate, covering it loosely with foil. Let it rest for 5 minutes, allowing the juices to redistribute for maximum tenderness. Finish by placing a pat of butter on top, letting it melt into the steak before serving.