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.
While the meat is roasting and resting, combine the cream, Parmesan, mustard and salt and pepper in a small saucepan. Heat over medium heat, whisking frequently for about 5 minutes until thickened.
Serve the filets with the sauce drizzled over, sliced if desired, and the rest of the sauce passed on the side.
Notes
Make sure your thermometer is positioned directly in the center of the steaks for the most accurate reading. Rare is 120 degrees and medium rare is 125 degrees. Remember that the steaks will continue cooking once they have removed to a cutting board, and you want to account for that carryover cooking. Nothing worse than overcooking a pricey cut of meat.