Heat a large heavy skillet, such as cast iron, over high heat. Add 1 tablespoon olive oil. Season the steak generously with salt and pepper. When the oil is hot, sear the steak for 3 minutes on each side, until a nice crust has formed.
Transfer the pan to the preheated oven and roast for about 6 to 9 minutes, until the steaks are done to your liking. The inside will read 120 F on an internal thermometer for rare, 125 F for medium rare. Transfer the steaks to a cutting board and let rest for at least 5 minutes.
Slice and serve.
Notes
Filet mignon is from the tenderloin part of the cow, a muscle that gets very little use, and therefore remains, as the name suggests, tender. It’s actually pretty lean, with little fat, but that doesn’t affect its softness. Pick filets that are fairly thick, about 1 ½ to 1 3/4-inches. Thinner filets run the risk of overcooking on the inside before the outer crusts have a chance to caramelize properly. Again, if you end up with thinner filets, just pan sear them and skip the roasting.