This is the way my favorite steak restaurants cook their filets. The filets are simply seasoned with salt and pepper, seared in a smokin' hot skillet in olive oil, then finished in a very hot oven. You will have a juicy filet with a nice crust on the outside and tender on the inside. It will absolutely melt in your mouth. There really isn't a recipe here...it's the technique that's important. I served some of my country style mac 'n cheese.
Filet Mignon - cut 2 inches thick
Preheat oven to 500 degrees. In a large skillet (cast iron if you have one), heat olive oil over high heat until it starts to slightly smoke and look wavy. Use a paper towel to dry steaks completely. This will help give you a nice sear on the outside. Season both sides with salt and pepper. When your oil is ready, add the steaks to the skillet. Cook until a nice brown crust forms. See the smokin' hot I was talking about...