Season the filets generously with salt at least an hour in advance. Ideally, do this the night before you plan to cook them.
Bring the steaks to room temperature before cooking. Take them out of the refrigerator at least 30 minutes before (or more if they are thick cuts). Season with black pepper.
Preheat the oven to 400°F.
Heat a large oven-proof skillet over high heat. Add the oil and swirl to coat the pan. Sear the steaks for about 2 minutes on each side.
Place the whole pan with the steaks in the oven. Monitor with a meat thermometer. For medium-rare it should take about 6 minutes. Remove from the oven when the internal temperature reaches 125°F.
Remove the steaks from heat and let them rest on a plate or cutting board for 5-10 minutes before slicing or serving. You can lightly tent them with foil to keep the warm.