Clean the filet. You can see how on the video above.
Put vegetable oil on a pan and bring to high temperature until it starts to smoke.
Sear the meat by laying it on one side and let it get golden without moving it. Once golden, rotate and repeat. Also sear the ends.
Take to a preheated oven at 180C for 20min for medium. Or even better, take it out when you measure with a meat thermometer that its core temperature reaches the one for the degree of cooking you like.
Once it has cooled down to room temperature, cut thin slices.