Cover your working space with a clean tablecloth. Dust hands with flour.
In a large mixing bowl combine flour, salt, and 2-3 tablespoon oil. Slowly add about 2 cups of warm water and start working the flour into dough. Fold, press, knead, push and punch the mixture just as if you were making bread or pizza. Keep adding water, a little at a time. (In total, you'll add about 3 cups of warm water, or about 700 ml.) Knead vigorously for 7-10 minutes or until the dough is elastic. The dough should feel between dry and sticky to touch. If too sticky, add a little more flour. If too dry, add a little more water. Finished dough should have the consistency of an earlobe.
Transfer dough onto your working space. Cut it in five equal parts. Knead each part for a few more minutes. Shape into a round, flat-ish, thick ball. Dab each dough ball with oil on all sides. Cover with a kitchen towel. Leave to rest AT LEAST 30 minutes.
Peel and finely dice or grate the potatoes. Peel and mince or grate the onion. Combine onion and potatoes with ground beef. Add salt, pepper and two tablespoons of oil. Mix with your hand until well integrated. Set aside.
Dust the working space generously with flour. Take one dough ball and knead it for a minute or two. Dust the ball with flour and get the rolling pin out.
If you have a thin rolling pin (aka oklagija), you’ll be able to roll the dough out quite a lot before working it with your hands. Roll the dough out on your working space until it’s the thickness of few stacked pennies, or the size of a large circle. Dab the dough lightly and evenly with oil (2-3 tablespoons). Position rolling pin in the middle of the circle as if you were measuring the diameter, and then transfer one half of the dough over the rolling pin. As you lift the pin dough will hang equally on both ends. Shake the pin so the dough doesn't stick to itself. (Oil should prevent this.) Unstick it if it does.
(If you have a thicker rolling pin, the process will be a little harder, but doable. Roll the dough out as much as you can, usually the size of an extra large pizza. Once you roll it as much as it will stretch with the pin, dab with oil lightly (1-2 tablespoons). Drape equally over the pin and lift the pin.)
Let the dough weigh itself down. After it’s stretched out as much as it will under its own weight, turn the dough 45 degrees on the pin so it stretches on the other side. Patch up any rips by pinching the dough together. While the dough is on the rolling pin, slowly and carefully stretch it out with your hands as far as it will go. Use knuckles to do this to prevent tears. The dough should now be the thinness of cigarette paper and the size of a super large circle (or an ellipse). If you're using a long rolling pin transfer the dough back onto your working area.
(If you are using a small, thick rolling pin, you may have to transfer the dough onto your arm in order to stretch it out more. Carefully take the dough off the pin and drape over one arm. Continue stretching the dough by pulling the dough ends with the top of the opposite hand. The pull is a slow, light and patient motion outward. If small rips occur, patch them up and continue. Continue this all around until the dough is of the thinness of cigarette paper and the size of a super large circle (or an ellipse).)
Dab the dough with oil lightly (1-2 tablespoons). Continue stretching the dough out with your hands a little more trying to keep the form. Avoid rips the best you can. If they happen patch them up.
If the dough is thick on the ends, cut half inch of dough ends with a knife. Discard. Grab batches of stuffing, and line the outskirts of the dough circle generously. (Use one fifth of the stuffing as you have another four dough balls to go.) Starting at any point, lift the end of the dough and cover the filling. Go around the dough circle covering all the filling. Dab the dough with oil again (1-2 tablespoons).
Once all the filling is covered, continue going around the circle and rolling the filling into the dough. Essentially you're rolling the dough with the filling toward the inside of the circle for a few inches, and then pulling it back toward yourself. Do this equally around the circle. After a few rounds of rolling, the dough will tear in the middle. Keep on rolling the dough until most of the middle is torn. Cut the remaining middle part out. You should be left with a large hula hoop or hose shaped dough stuffed with filling.
Cut the dough at one end and start making small spiral rounds. (You can also fill the middle remainder of the dough and form it into a round.) Spiral rounds are made by circling the dough around itself a couple of times and cutting it away from the hose. Each long hose should give you 8 pie rounds. Place rounds into an oiled pan. Dab the top of each round with oil.
Preheat oven to 460°F. Repeat steps 5 through 13 for the remaining dough balls. (You may have to bake in batches. Do not bake two batches at once in the same oven!)
Place pan on medium rack and bake 20 minutes or until golden on top. Lower heat to 375°F, and bake an additional 10-20 minutes. If at any point pita gets too brown on top, cover with foil and bake an additional few more minutes. Turn the oven off.
Boil 1-2 cups of water with 2-3 tablespoons of butter. Sprinkle generously over pita. Wait for it to cool, then serve.