Preheat your oven to 400°F.
Pat the filet mignon steaks dry with paper towels. Generously season with salt and black pepper.
2 (8-ounce) filet mignon steaks, ½ teaspoon kosher salt, ½ teaspoon freshly ground black pepper
In an oven-safe skillet, heat oil over high heat until it lightly smokes. Add the filet mignon steaks and sear for 3 minutes on each side until browned. Turn the heat off and add the thyme, garlic, and butter.
2 tablespoons vegetable oil, 2 sprigs fresh thyme, 2 cloves garlic, 2 tablespoons unsalted butter
Transfer the skillet to the preheated oven and roast for about 10 minutes for medium-rare or adjust the time based on your desired doneness (135°F for medium-rare, 145°F for medium). Flip halfway through. Remove the steaks from the oven when the internal temperature is 10°F below your target, as it will rise during the rest.
After taking the skillet out of the oven, transfer the steaks to a plate or cutting board, allowing them to rest for 5 minutes.