Dissolve the yeast cube in the cool water, add 1 tbsp flour and the sugar. Once the yeast activates, pour it into the sifted flour.
Add 1/2 the melted butter, the yoghurt, salt and break in the eggs. Stir using a spoon until you start to get crumbs. Begin kneading until you obtain a smooth and soft dough. If needed, add a little more water or flour.
Leave the dough to rise, covered with a towel. Once the dough doubles in volume, divide it into 4 balls.
Roll out each ball into a sheet, smear with melted butter, sprinkle with crumbled feta cheese. Place the sheets on top of one another and wrap into a roll. Cut the roll into pieces, fold each piece in 2 and arrange them in a tray with a nonstick bottom.
Leave the pita to rise again. Smear it on top with beaten egg yolk and bake in a moderate preheated oven until golden.