For the Filling:
Mix the flour, whipped egg, water, yeast and mashed potato with an electric mixer until you get a firm, smooth dough. You can add more warm water if needed. Leave the dough to rest in a warm place. For the filling: crumble the feta cheese with a fork and combine it with the parsley and onion in a bowl. On a lightly floured surface, roll the dough using a rolling pin. Cut the dough into 8 cm diameter circles using a circular pastry cutter.
Coat the border of the dough circles with a bit of egg white, and fill each circle with 1 tablespoon of the cheese mixture then seal firmly its 4 edges to form a square that holds the cheese. The cheese should remain visible in the middle. Place the cheese pies on lightly greased oven pans and bake at medium heat until they turn lightly brown. Serve hot or cold.