Combine the flour, yeast, salt, sugar, 1 cup of the water, and the olive oil in a food processor. Pulse just until a ball forms.

With the machine running, stream in the remaining 3 tablespoons water and process for 1 minute. The dough should be loose and sticky.

Scoop the dough into a large bowl and cover with a kitchen towel. Let rise at room temperature for 30 to 45 minutes, or until doubled in volume.

Place a baking stone or upside-down baking sheet on a rack in the bottom third of the oven and preheat the oven to 500°F (or as high as it will go).

Once the dough has finished rising, transfer to the refrigerator and let rest for at least 15 minutes or up to 3 hours.

Remove and scrape the dough onto a lightly floured board. Pat it into a log shape, then cut it into 4 equal pieces using just enough flour to keep it from sticking.

Form each piece into a round by gently tucking the edges underneath, making sure to smooth the top.

Transfer the whole board to the refrigerator for at least 10 minutes or up to 2 hours to relax the dough.

Remove the dough from the refrigerator and use a rolling pin or the palm of your hand to gently flatten each round into a 4- to 6-inch disk.

Place the disks on the hot stone or baking sheet in the oven and bake for 3 to 5 minutes, or until they are puffed and light brown on top.

Remove the pitas from the oven and wrap them in a kitchen towel for 5 minutes before serving.