Remove filets from refrigerator and allow to sit at room temperature for 30 minutes.

Heat oil in a large cast iron pan over medium-high heat. Pat steaks dry with a paper towel to remove any moisture.  

Evenly season with salt and pepper and carefully add to pan. Sear for 2 minutes without disturbing the pan. Flip steaks and sear an additional 2 minutes. Add butter, thyme and garlic to pan. Using a spoon, baste the steaks for 1 additional minute.  

Remove steaks to a plate and sprinkle with sea salt. Cover with aluminum foil and let rest for 5 minutes.