Here's what I do to cook 2" filets in a skillet.
- Preheat the oven to 400 F (use the bake function)
- Heat your skillet on high heat until a droplet of water flipped into the pan dances around on the surface.
- Add enough canola, peanut or corn oil to just cover the pan bottom.
- Wait until the oil gets hot - it will start to shimmer.
- Season and place the two steaks into the pan with at least 1" of space between them. Let them cook undisturbed for 2-2.5 minutes. That means don't try to move them.
- Turn the steaks over and cook them undisturbed for 2-2.5 minutes.
- Place the pan, with the steaks, into the oven for 9-10 minutes for rare, 10-11 minutes for medium rare to medium.
- Remove the pan from the oven and move the steaks to a plate.
- Tent the steaks with foil and let them rest for ten minutes.
You will be adding the meat to the pan before the oil smokes. The coldness of the meat relative to the temperature of the pan will cool down the pan and the oil so it won't smoke.
If your skillet isn't ovenproof at 400 F, be prepared to transfer the steaks to a shallow pan for the oven part of the process. A pie plate will do.