Add all the ingredients for the dough into a large mixing bowl, knead it with your hands or in a stand mixer with a hook attachment until it reaches a smooth consistency, cover it with a damp cloth, and let it rest for at least half an hour.
On the other hand, mix all the ingredients for the stuffing in another mixing bowl and set it aside.
Divide the rested dough into 4 equal parts and roll them into balls with your hands.
Roll out each ball approximately 20 cm/8 inches long and 10-12 cm/4-5 inches wide. Try to use flour sparingly when rolling out the dough. Cover the other balls with a cloth when rolling out the dough so they do not dry out. Put the stuffing you prepared in the middle of the pide and spread it evenly, leaving 1 cm/0.5 inches of space around the edges.
Fold the edges over the cheeses. Refrain from rounding the ends of the pide, and fold it in a pointed way.
Take it to the tray you have floured the bottom of.
Whisk the egg yolk and water together and brush the edges of the pides.
Bake the pides in a preheated oven at 230°C/450°F for the first 10 minutes on the bottom shelf and the next 7 minutes on the middle shelf for about 17 minutes in total until golden brown.