In the bowl of a stand mixer, combine water, honey, and yeast. Let it sit for about 5 minutes until foamy.
Add the flour, salt, and olive oil. Mix for a couple of minutes until the dough comes together.
Turn it out onto a floured surface and knead for about 5 minutes until smooth. Add a little extra flour if it’s too sticky.
Shape it into a ball, place it in a lightly oiled bowl, cover it, and let it rise somewhere warm until it doubles in size. This takes about an hour.
Punch down the dough and divide it into 9 equal pieces. Shape each one into a ball.
Working with one at a time, roll it into a thin circle, about ¼ inch thick. Turn the dough as you roll to keep it from sticking. Add a bit of flour if needed.
Keep the rest of the dough and rolled circles covered with a towel or plastic wrap so they don’t dry out.
Preheat the oven to 450°F (230°C). Place a baking stone or upside-down baking sheet in the oven and let it heat for at least 20 minutes.
Bake a few pitas at a time for 4 to 5 minutes until they puff up and start turning golden.
Transfer to a wire rack for a few minutes, then wrap in a clean towel to keep them soft. Let them cool slightly before cutting.
