Make pita like a pro

Anyone who comes from a pita-rich country to North America knows that you really can’t get your hands on good pita here. I came across a recipe in Hebrew that is really good, and makes fantastic doughy pitas with nice pockets.
You need:

In a large bowl, sift in the flour and mix all the dry ingredients (salt, sugar, yeast) until it is all evenly distributed. Add the olive oil, and half the the warm water. Start mixing with a spoon, and add the rest of the water slowly.
Now it’s time to get dirty (if you haven’t gotten flower on everything already). With a wet hand, reach into the bowl, and knead the dough in a twisting fashion, as if you were screwing a light bulb. If the business gets sticky, re-wet your hand as many times as needed. Does your arm hurt yet? Good. Keep twist-kneading, and switch directions every once in a while. Do this for 10 minutes.
Set the bowl aside, and let the dough rise for an hour and a half until it doubles in size.
Put pizza stone in oven and preheat it to its max temperature, my oven goes to 550 degrees F. The dough, once risen should be very airy and wet. This is good! Spill it out to a floured work surface and get control over it with flour. Now use a knife to split the dough into 16 balls. Flatten each ball with a rolling pin to create flat circles.
Baking time! Each pita will need about 2 or 3 minutes, not more. If you are seeing any browning you are a few seconds late. You should see the pita puff up and get a pocket. I managed to bake two at a time, and have a huge basket filled with fresh pita in about 15 minutes.