Take the filet mignon steaks out of the refrigerator and let them sit at room temperature for about 30 minutes. This helps them cook more evenly.
Pat the steaks dry with paper towels to remove any excess moisture. Season both sides generously with salt and pepper.
Heat a heavy-bottomed skillet (preferably cast iron) over medium-high heat. Add the olive oil to the skillet and swirl to coat the bottom evenly.
Once the skillet is hot, carefully place the filet mignon steaks in the skillet. Make sure they are not crowded; you want some space between them to ensure even cooking.
Sear the steaks for about 3-4 minutes on one side without moving them. This will give them a nice crust.
Flip the steaks using tongs and sear for an additional 3-4 minutes on the other side. If you prefer your steaks rare, reduce the cooking time slightly.
Optional: Add the butter and any minced garlic or herbs to the skillet during the last minute of cooking. Tilt the skillet slightly and use a spoon to baste the steaks with the melted butter and aromatics.
Once the steaks reach your desired level of doneness, remove them from the skillet and transfer to a plate. Let the steaks rest for about 5 minutes before serving to allow the juices to redistribute.
Serve the pan-seared filet mignon steaks with your favorite side dishes, such as mashed potatoes, roasted vegetables, or a simple salad.