Peel the potatoes, wash them and put them to boil in salted water for about 20 min. after boiling point (on low) or until ready. Drain them and leave them to cool for 1-2 min.
Heat 1/4 cup oil in a pan on medium heat and braise the onions until softened, stirring for about 5 min.
Heat the oven to 374°F (190 °C) and lay out a large tray with baking paper.
Whip the eggs, 1/2 cup oil and 1 tsp salt. Gradually add the flour and mix a dough. Transfer it to a floured kitchen counter and knead for about 8 min. - it needs to become smooth and elastic.
Divide the dough into 3 parts, forming each one into a roll. Roll out each roll to a size of about 8″ x 12″ (20 x 30 cm) and cut them in half lengthwise. Put some of the potato mixture lengthwise in the middle of each strip and carefully form a roll. You need to end up with 6 rolls.
Cut each roll into 1 (3 cm) pieces and arrange them with the cut side facing down in the tray. Carefully press the ends of the pitas toward the middle with the potato filling. Smear the pitas with the egg yolks beaten with milk and bake in the preheated oven for about 35-45 min.