Pour 3 tbsp of the oil in the dough. Toward the end of kneading, stretch it out and pour in another 2 tbsp oil.
Knead well until the oil is absorbed by the dough. Do this twice. Leave the dough to rise well about 1 hour. Then tear 2 equal-sized small parts, about 4 oz (120 g) each, from it.
Roll out 1 part to an ellipse with a thickness of 1/4″ (0.5 cm), pour oil over it and shape into a roll. Roll the other one out to the same length, cut 1/2″ (1 cm) identical strips in the middle. Take the topmost strip and slide it in through to the next one. Place thus formed woven pita on top of the roll and finish shaping it.
Place it at one end of a 12 1/2″ (32 cm) diameter baking tray that's covered with baking paper. Make another woven roll the same way, place it across from the 1st roll. Then tear a part from the dough and roll it out into a rectangle.
Cut strips at one end of it - they need to be about 8″ (20 cm) long. Smear the uncut part with oil. Grab the strips 3 at a time and weave them together. Thus formed, wrap the sheet into a roll, make sure to have the weaves on the underside.
Put the roll underneath the other rolls in the middle of the tray. Tear off a ball from the dough to make the middle, as well as another small one to roll out and cut forms out from. Place them on top of the ball and place in the middle of the pita.
Divide the remaining dough into 4 parts and roll out sheets from it. Smear them with oil, arrange on top of one another and stretch slightly with your hands. Cut the sheets into 8 parts, make a cut in the middle of each. Stick the vertex through the hole from the bottom going up and shape into a leaf.
Arrange 3 leaves along each of the empty sides in the tray. Leave the pita about 20 min. to rise a bit, then smear it with egg yolks all over. Place it in a cold oven, turn it up to 356°F (180 °C) and bake about 40-45 min.