I've made pitas a few times, but never posted here. Freshly baked pitas are absolutely delicious, I never knew they could be so tasty when I used to have them from the supermarket.
Basically, I make them using sourdough, with 20% whole grain (and I think I've only used spelt in this case), and 65% hydration, some olive oil and a bit of sugar. Here is the formula: https://fgbc.dk/1m2j
I mix all ingredients except for oil and develop a little strength, and then knead in the oil. I doubt it's really necessary and the oil can probably be kneaded from the beginning with no problems. I then let it rise until nicely puffy, and due to the nature of this bread there is no specific volume increase or any other target - just until looks and feels good. Then, since I mostly use them for breakfast with hummus, I just put the dough in the fridge until morning. In the morning I start by turning on the oven with the baking steel in and preheat on the highest temperature for about 30 min. While it's preheating, I scale and ball up the needed amount of pitas (the formula above makes about 8 generously sized 115 g pitas). If I feel like it and have enough space in the container, I might ball up all of the dough and put extra balls back in the fridge to save time next day. The dough keeps in the fridge exceptionally well, I've certainly kept it for 3 days with no issues.
After 15-20 min of preheating, I roll out the pitas into thin rounds (or whatever shape I manage). From reading some old discussions here and from my experience, nice balling up like for pizza, and careful rolling out is very important for good inflation. Letting the dough rest at either the ball or the flat stage also helps a lot, and for me roughly 30 min total time works well. When ready to eat, I just place one or two pitas on the steel at a time and switch on the grill. Then hopefully the pitas puff up like balloons, and the top gets a little nice browning from the grill (but it is easy to overcook them and make the top too dry). Here is a video of the cooking in real time: https://photos.app.goo.gl/dPH1Mn74NrhHwUSq7 (I started it a few seconds after placing the dough on the steel, and the time needed to turn on the camera already was enough for a lot of bubbling!). (The picture on top is from a different batch a while ago.) The flavour is fantastic.
The only minor issue is that I get a much thinner and less fluffy inside top relative to the bottom of the pita, like so:
I wonder what I could do to make them more even? I am really happy with the results every time nevertheless.
As a bonus, it seems cooking them on the grates instead of the steel produces Greek-style pitas, which are more fluffy and don't have a pocket. But that needs more experimentation, I've only done this once when I brought this dough to a barbecue hoping to cook on the grill, but due to weather it was moved indoors and I cooked on the grates in a gas grill oven.