You need a spiral cutter (e.g. from Lurch) for this.
Peel the potatoes and cut into fine endless spirals with the spiral cutter.
Cut the feta into small blocks and then wrap the potato spirals around it so that the cheese does not come into contact with the pan. Then heat the oil and fry the parcels until crispy on all sides. The cheese won`t run if the fat is hot and you turn it over as soon as the potatoes are nice and brown. Then you can add salt if you want. But economical, as the feta is naturally very salty.
Tastes warm when the cheese is a little softer, but can also be eaten cold. I like them best when they are lukewarm.