Preheat the oven to 120 °. Halve the fillet and season with salt. Peel the garlic and cut in half lengthways. Heat a pan. When it is well hot, add about 2 tablespoons of neutral oil and garlic and fry both pieces of fillet very hot all around. Then immediately remove it from the pan, attach a thermometer to one and then place both on the grid in the oven. The core temperature for "medium" should be 55 - 59 °. (Rare = still very pink inside 52 - 55 °). But since it is then fried again with the jacket in the pan, it should be removed shortly before the end of the desired cooking time.
While the meat is lingering in the oven, grate the peeled potatoes finely (I used a julienne slicer, a different one, but finer is also possible. Then put the mixture in a kitchen towel, squeeze out a little and mix with the egg white in a bowl pepper and salt.
When the meat is about 5 degrees from its desired finish, remove it from the oven. Spread out enough potato mixture on each of 2 other kitchen towels so that the two pieces of fillet can be wrapped tightly in them. This has to be done with pressure, otherwise the cover will fall off again. When both are coated, heat a little more oil in the pan and fry both coats all around until crispy.
Briefly heat the mash and carrots again, arrange everything together and .............. enjoy.