Preheat your oven to 400°F (200°C).

Heat the olive oil in a large oven-safe skillet over medium-high heat. Pat the steaks dry with a paper towel and generously season both sides with kosher salt and freshly ground black pepper.

Once the oil begins to shimmer and nearly reaches the smoking point, carefully place the steaks in the skillet. Sear the filets without moving them for about 5 minutes until a rich, golden-brown crust forms. Flip the steaks and immediately add the butter and chopped rosemary to the pan.

Tilt the skillet slightly and begin basting the steaks with the melted herb-infused butter, using a spoon to coat them thoroughly. Continue cooking for an additional 3 to 5 minutes, depending on the desired doneness.

Transfer the entire skillet to the preheated oven and roast for roughly 5 minutes for medium doneness. For greater precision, use a meat thermometer before oven-finishing: if the internal temperature is within 10°F of your target, reduce oven time accordingly. If more time is needed, check frequently in short intervals to avoid overcooking.

Once done, remove the steaks from the skillet and let them rest for 5 minutes on a cutting board before slicing. This allows the juices to redistribute, ensuring tender, flavorful results.