Because of it's tail shape, you will end up with a scale of doneness, with the fatter end being pinker than the thin end.
Remove the meat from the fridge half an hour before cooking.
Season the steak liberally with sea salt and pepper, then rub with olicve oil.
Heat a heavy-bottomed frying pan over a medium-high heat.
Sear the fillet all over, until browned, and transfer the pan to the oven for 6 minutes.
With a meat thermometer, check for an internal temperature of 50 degrees c at the fattest point.
Remove from the oven and add the butter to the pan with the garlic and herbs. Baste for a few minutes, then remove the steak from the pan to rest for 5 minutes.
Chimichurri is a great accompanying sauce for a steak with low fat content, such as fillet.