Begin by running your fingers between the main part of the meat and the thick bit of connective tissue which is known as the chain. This will come away from the main part of the meat, which you will need to run your knife through to separate completely. The chain can be used for mince or to make a sauce.
Next, remove any membrane from the top of the fillet to expose the silverskin. This is the tough sinew that does not break down during cooking and is best removed. To do this, insert a knife under the pointed end of the silverskin a few centimeters from the end and, pointing your knife upwards, free the tip of the sinew.
Turn your knife around and place it under the flap you have just created. With your knife facing upwards away from the meat, run it all the way along with the meat in one long slicing motion to the end until all of the silver-skins are freed.
Repeat this process until the meat is completely clear of the silver-skin. It is important to face the knife upwards to avoid cutting into the fillet and losing any meat.
There will also be a small piece of silver-skin on the back of the fillet which should also be removed in the same way.
Remove any excess or loose pieces of fat from the beef fillet, do not cut away all of the fat as this will render and give flavor to the meat as it cooks.
Cut off the pointed end of the fillet until the meat is of an even thickness.
For Roasting the Fillet:
Preheat the oven to 445°F / 230°C
Spread the mustard evenly on all sides of the fillet. Sprinkle with salt, pepper, and thyme.
Heat the oil in an ovenproof skillet over high heat, the oil should be hot but not smoking. Brown the fillet on all sides, 2 to 3 minutes per side. Place the fillet in the oven and reduce temperature to 400 degrees F/ degrees 205C. Roast for about 25 minutes for rare or until it is to your liking. Remove the fillet from the oven and allow it to rest 10 minutes before slicing.