This is my favourite way to cook fillet.
Rub fillet medallions with olive oil and season generously with salt and pepper.
Preheat a grill pan for about 5 minutes so that the entire surface of the pan is completely heated, do not add any oil to the pan.
Place medallions into the pan one at a time making sure to not over crowd the pan. There should be a lot of sizzling as the steak touches the pan, cook for a few minutes then turn steaks around.
(Tip: after placing steaks into the pan do not move them around to ensure a nice crispy coating forms) After another minute or 2 add a tablespoon of butter and once melted in the pan drizzle over the steaks with a spoon.
Remove from heat and allow to rest for a few minutes before serving.