Stir in the salt. Add the flour, a little at a time, mixing at the lowest speed until all the flour has been incorporated and the dough gathers into a ball; this should take about 4 minutes.
Turn the dough onto a lightly floured surface and knead until it's smooth and elastic. Transfer the dough to a lightly oiled bowl, turn it over to coat, and cover with plastic wrap. Allow to rise until double in size, about 1 1/2 hours.
Place a large pizza stone on the lower oven rack, preheat the oven (and stone) to 500 degrees F.
Punch the dough down, divide it into 8 pieces, and gather each piece into a ball; keeping all of them lightly floured and covered while you work. Allow the balls of dough to rest, covered, for 15 minutes so they will be easier to roll out.
Using a rolling pin, roll each dough ball into a circle that is about 8-inches in diameter and 1/4-inch thick. Make sure the circle is totally smooth, with no creases or seams in the dough, which can prevent the pitas from puffing up properly. Cover the disks as you roll them out, but do not stack them up. Put 2 pita rounds at a time on the hot pizza stone and bake for 3 to 4 minutes, or until the bread puffs up like a balloon and is pale golden. Watch closely; they bake fast. Remove the bread from the oven and place on a rack to cool for 5 minutes; they will naturally deflate, leaving a pocket in the center. Wrap the pitas in a large kitchen towel to keep them soft.
Recipe courtesy Tyler Florence and JoAnn Cianciulli