In a large bread bowl, sprinkle the yeast over the warm water. Stir to dissolve. Stir in 3 cups flour, a cup at a time, and then stir 100 times, about 1 minute, in the same direction to activate the gluten. Let this sponge rest for at least 10 minutes, or as long as 2 hours.
Sprinkle the salt over the sponge and stir in the olive oil. Mix well. Add more flour, a cup at a time, until the dough is too stiff to stir. Turn it out onto a lightly floured surface and knead for 8 to 10 minutes, until smooth and elastic (I found that after 10 minutes of kneading by hand the dough still wasn't ready, so I transferred to my Kitchen Aid with a dough hook for another 5 minutes). Rinse out the bowl, dry, and lightly oil. Return the dough to the bowl and cover with plastic wrap. Let rise until at least doubled in size, approximately 1 ½ hours.
Place a pizza stone, or two small baking sheets, on the bottom rack of your oven, leaving a 1-inch gap all around between the stone or sheets and the oven walls to allow heat to circulate. Preheat the oven to 450°F.
Gently punch down the dough. Divide the dough in half, and then set half aside, covered, while you work with the rest. Divide the other half into 8 equal pieces and flatten each piece with lightly floured hands. Roll out each piece to a circle 8 to 9 inches in diameter and less than 1/4 inch thick. Keep the rolled-out breads covered until ready to bake, but do not stack.
Place 2 breads, or more if your oven is large enough, on the stone or baking sheets, and bake for 2 to 3 minutes, or until each bread has gone into a full balloon. If for some reason your bread doesn't puff up, don't worry it should still taste delicious. Wrap the baked breads together in a large kitchen towel to keep them warm and soft while you bake the remaining rolled-out breads. Then repeat with the rest of the dough.