For this dish it is advisable to buy black pepper already ground, because you need lots of it. To grate the amount needed with a pepper mill takes a major effort. Clean your filet, wash it and pat it dry with a kitchen towel. Spread the ground pepper on a flat plate and roll the filet in it, so it is covered on all sides by black pepper. Now heat the oil in a large pan with a lid and fry the filet on all sides. Add the port wine and a glass of water. Then close the pan with a lid and let simmer on lowest flame for around 2 hours.
You can also use a pressure cooker. Follow the same procedure, close the cooker and let the filet boil for around one hour after the first whistle. At the end of the cooking time, add salt according to your taste and the butter. With a pressure cooker, wait until the pressure drops then add the salt and the butter. Take the meat out from its sauce and let it rest for half an hour before cutting. If you try to cut the beef immediately after cooking it is very difficult to cut properly. Carve up the filet into thin slices, arrange the slices on a plate and pour the sauce over it. Serve immediately with boiled potatoes or toasted bread and vegetables of your choice.
I usually prepare this dish one day before I want to serve it. After one night in the fridge it is very easy to slice the meat perfectly. I arrange it cold on a plate and heat up only the sauce before serving.