Preparation: Take the Filet Mignon steaks out of the refrigerator 30 minutes before cooking to bring them to room temperature. Pat them dry with paper towels and season generously with salt and pepper.
Searing the Steaks: Heat a large cast-iron skillet over medium-high heat. Add olive oil and heat until shimmering but not smoking. Place the steaks in the skillet and sear for 4-5 minutes on each side for medium-rare, or adjust time according to desired doneness.
Adding Flavor: During the last minute of cooking, add minced garlic, butter, and thyme to the skillet. Baste the steaks with the melted butter and aromatics continuously.
Resting: Remove the steaks from the skillet and let them rest on a cutting board or plate tented with foil for 5-10 minutes. This allows the juices to redistribute and ensures a juicy steak.
Serving: Slice the Filet Mignon steaks against the grain and serve immediately, drizzling with any remaining pan juices and butter.