Season tenderloin on all sides with salt and pepper. Heat oil over medium-high heat in a large saute pan with an oven safe handle and when oil is hot, sear beef on all sides. (Leave undisturbed for the first 2 minutes or so as you sear each side to allow the seasonings to integrate into the surface of the meat and to allow the caramelization process to begin.)
Transfer entire pan to the oven to finish until meat thermometer reaches an internal temperature of about 118 degrees F and pull out to let rest and carryover cook to an internal temperature of 132 degrees or so for medium-rare as measured on a meat thermometer, or cook until done to your liking. Slice into medallions after the meat has rested.