heat an oven safe pan (I prefer cast iron) on the stove top with oil.
when it's nice and hot sprinkle some salt and pepper in the pan and add the filet.
Don't move it, cook for 2 1/2 mins.
Then, using tongs, flip the filet and cook for another 2 1/2 mins.
Flip the filet again and put the whole pan in the oven.
Bake for 4-10 mins depending on if you want it rare (4), medium rare (my choice- 5 mins), medium (6), medium well (8) and well (10). I use the finger test or you could use a thermometer
I like to flip it once during the cook time.
Once it's done pull it out, wrap it in foil and let it sit for 5 mins.