Let the steaks sit at room temperature for at least 30 minutes before cooking.
Season the steaks with salt and pepper on both sides.
Heat a cast iron skillet over medium-high heat and add olive oil.
Once the oil is hot, add the steaks and sear for 3-4 minutes on each side until a brown crust forms.
Add butter, garlic, and rosemary to the skillet. Baste the steaks with the melted butter using a spoon.
Transfer the skillet to a preheated oven at 400°F (200°C) and cook for another 5-6 minutes for medium-rare.
Remove the steaks from the oven and let them rest for 5 minutes before serving.
Notes
For a perfect medium-rare filet mignon, use a meat thermometer to ensure the internal temperature is around 135°F (57°C) before removing from the oven.