Remove the filet mignon from the refrigerator 30-60 minutes ahead of time, so they can reach room temperature for more even cooking.
Preheat your oven to 425°F, putting the rack in the middle position.
Place a large cast-iron skillet over high heat and allow to heat for 5 minutes until very hot, using oven mitts at all times.
Pat dry the steak with paper towels to remove excess moisture. Then rub on all sides with 1 tablespoon of oil followed by the salt and pepper.
Add the remaining 1 tablespoon oil to the pan and swirl to coat.
Carefully place the filet mignons in the pan using tongs. Sear the first side for 2 minutes undisturbed. Then flip and sear the other side for 2 minutes more.
Add the garlic, butter and optional rosemary to the pan. Then transfer to the oven.
Bake for without flipping for about 2-10 minutes depending on your desired doneness, measuring the internal temperature using an instant-read thermometer. Medium rare will measure 125-130°F and take 4-5 minutes although times vary by thickness (see note).
Let the filet rest for 5 minutes on a plate tented with foil to keep warm. This step allows the juices to retreat back in to the meat for maximum tenderness before serving.