I wouldn't like to heat the oven just for making a pita bread for one sandwich. Could I bake it entirely in just a pan, just like some tortilla?
The answer is almost certainly yes.
The almost is because I haven't made pita bread this way - but I have seen chapati made on a skillet, and under the right conditions it will puff up, even into one big pocket - so pan cooking doesn't specifically preclude that kind of development. Beyond the need for it to puff up into the pocket, I don't imagine pan-cooking pita bread is that much different form other kinds of pan-cooked flat-breads.
it looks like cast iron is preferred, since it can be heated very hot and has the thermal mass to hold the heat steady while the pitas are cooking - but I honestly expect you can make them with any skillet you have on hand. Stove-top pitas may be a touch drier, slightly less puffy, but have more browning (and toasty-flavor) than oven-baked pitas, because they're in direct contact with the heat, instead of being cooked by radiant heat. You can press the surface gently with a clean towel to help the pocket form if it isn't forming quickly or fully enough for your tastes.
I do this all the time; I keep dough in the fridge and can turn it into a pita in five minutes.
My preferred way of doing it is to preheat a cast iron pan (which I do as I roll out the dough), put in the round of dough, and then slide it under the broiler. Heating it from both sides ensures perfect results every time.
I have had a bit less success doing it purely on the stovetop. The trick is that you need to cook both outside before the inside cooks too much (which would prevent it from puffing properly). The timing is a bit of a knack and will depend on the dough, your pan, etc. So I can just give you some general advice:
- Preheat the pan over medium heat
- Put the dough in the pan
- Let cook 30 seconds to 1 minute
- Flip it over.
- Cover it. Let cook 30 seconds to 1 minute.
- It should now be slightly puffy, but not very brown on either side.
- Flip it again. Cover.
- Cook until it is well puffed, another minute or two
- Take it out. Let it rest 3-5 minutes. (It's full of very hot steam, which will finish cooking the inside.)
- Open carefully: it's still full of very hot steam.
- Store in a plastic bag (to keep it from drying out).
If it doesn't puff fully... eat it anyway. It's cooked. It's just not doing the pita thing.