Adjust oven racks to upper and lower-middle positions. Place a cast-iron or oven-safe skillet in oven and preheat oven to 375 degrees.
Meanwhile, pat steaks dry thoroughly with a paper towel. Season on all sides generously with salt and freshly ground black pepper.
Carefully remove skillet from oven and place over medium-high heat. Add butter, garlic, thyme, and rosemary, swirling to combine the spices as the butter melts.
Add steaks, and sear until a good crust forms, about 3 to 4 minutes, basting with butter occasionally. Flip steaks and sear other side, about 3 to 4 minutes more. Using tongs, sear all sides of the steak, about 30 seconds.
Place steaks in skillet in oven, and cook until desired temperature is reached, 3 to 5 minutes for medium-rare (an internal temperature of 130 to 135 degrees), 5 to 7 minutes for medium (140 to 145 degrees) or 8 to 10 minutes for medium-well (150 degrees). Remove steaks from skillet and rest 5 minutes before serving.
Notes
Filet mignon: To substitute a different steak such as New York Strip or sirloin, trim as needed, then be sure to sear on all sides (including the edges with the white fat). Always let your steaks come to room temperature before cooking.
Yield: This Filet Mignon recipe is for two main entrees, but it easily doubles or triples to feed more guests.
Storage: Store leftover steak covered in the refrigerator for up to 3 days.