Pour the water, egg, oil, vinegar and salt in a bowl, gradually start adding flour. Knead a medium hard dough, divide it into 30-36 balls.
Roll out each ball into a small pita and arrange them in 2 piles of 15 stacked sheets each, smearing between them with butter. From the resulting piles, roll out 2 large sheets.
Put 1 in a buttered tray, sprinkle with crumbled feta cheese that you've beaten with 2 eggs, place the 2nd sheet on top.
Pour the remaining melted butter on top and put it to bake in a high oven.