Preheat your oven to 425°F, and place the rack in the middle position.
Place a cast-iron skillet over high heat. Let it heat for 5 minutes or until very hot, using oven mitts at all times.
Pat dry the steak with paper towels to remove excess moisture.
Rub on all sides with 1/2 tablespoon of oil. Then season with salt and pepper.
Add the remaining oil to the pan. Then carefully add the filet mignons into the pan.
Sear the first side for 2 minutes undisturbed.
Add the garlic, butter, and rosemary to the pan. Then flip and sear the other side for 2 more minutes.
Transfer the skillet to the oven. Bake for about 5-8 minutes depending on your desired doneness. If you prefer medium rare, it will take about 5 minutes. Measure the internal temperature using an instant-read thermometer. Medium rare will measure 125-130°F.
Once cooked, remove the steak from the oven, and let it rest for 5 minutes on a plate. Slice against the grain, serve, and enjoy!