Combine the flour, olive oil, yeast, salt, and sugar in a food processor.
Turn the machine on and slowly add 1 cup (240 ml) of warm water through the feed tube until a slightly sticky ball of dough forms, about 30 seconds.
Turn the dough onto a lightly floured surface and knead for a minute until smooth.
Place the dough in a lightly oiled bowl, cover with plastic wrap, and let it rise in a warm spot until doubled in size, about 1 to 2 hours.
Gently deflate the dough and divide it into 6 to 12 equal pieces, depending on your desired pita size.
Roll each piece into a smooth ball.
Place the dough balls on a floured surface, sprinkle with a little more flour, and cover with a clean towel.
Let them rest and puff up slightly, about 20 minutes.
While the dough rests, preheat your oven to 350°F (175°C). If using a pizza stone, place it in the oven to preheat. Otherwise, have a baking sheet ready.
On a floured surface, roll each dough ball into a thin round, less than 1/4-inch thick.
Bake the pitas for 5 to 8 minutes.
Place them directly on the hot pizza stone or on the baking sheet. They are ready when they have puffed up and are lightly browned in spots.
Flip them once halfway through baking.
As the pitas come out of the oven, brush them with optional melted butter or olive oil.
Serve warm or let cool and store in an airtight bag.
