Dissolve yeast and honey in ½ cup warm water. It needs about 5 minutes to activate.
Meanwhile, in a large mixing bowl, combine all the ingredients (water, water with yeast and honey, vinegar, salt, flour). Knead the dough in the bowl for about 10 minutes until it becomes smooth. Add very small amounts of extra hard flour if the dough is extremely sticky. Alternatively, knead the dough at medium speed in a stand mixer fitted with the dough hook attachment about 5 minutes. Don’t over knead it.
Cover the bowl with a damp kitchen towel and let it rise (double its size) in a warm place for 30 minutes to 1 hour.
When the dough has doubled, punch it down and transfer to a lightly floured work surface. Use durum or semolina flour for rolling. Divide the dough into equal balls (about 13 for large pitas and 25 for mini pitas).
Roll each piece into a circle, no more than ¼ inch thick taking care not to tear the dough and keeping the thickness even all around. It doesn’t need to be perfect. Use a round cutter or just a plate to cut into even pieces and get neat edges (optional).
Heat a large cast-iron skillet over medium-high heat and drizzle with olive oil. Place each piece and cook for about one minute. Several air pockets puff up. Be careful not to burn it because the skillet is extremely hot. Flip and cook for another 1 minute. Remove from the skillet and wrap in a kitchen towel. Repeat with the rest of the dough wrapped in a kitchen towel until cold.
Keep your pitas stored in a food container for up to 3-4 days or freeze for up to 2 months.