In a large bowl, whisk together the water and sugar to dissolve. Sprinkle in the yeast and let it sit for around 10 minutes (until it activates - it will foam up).

Add the salt and olive oil to the yeast mixture, stir, and add the 4 cups of flour. Stir with a wooden spoon until it gets too difficult before transferring the dough to a clean, well-floured surface.

Knead the dough using the palms of your hands until it is smooth and elastic but still sticky, adding a but more flour as needed to prevent the dough from sticking to your hands (around 1/4 cup or a bit more). Form the dough into a smooth round ball, place in a clean medium greased bowl, cover with a clean dish towel and let it sit in a warm draft-free spot until doubled, around 2 hours.

Line 2 large baking sheets with parchment paper. Gently deflate the dough and divide the dough into 12-16 balls of dough (depending on how large you want your pitas to be). Form each piece of dough into a smooth ball and, using a rolling pin, flatten slightly until the pitas are 1/4-1/2" thick. Repeat with the remaining dough and place the flattened pitas on the baking sheets, about 1" apart. Cover with plastic wrap or a slightly damp clean dish cloth and set aside to rest for 30 minutes. Meanwhile, preheat the oven to 500F

Once the pitas have rested, bake for 8-10 minutes, until puffed up and very lightly browned. Serve immediately.