In a large mixing bowl, combine warm water, sourdough discard (or active starter), and olive oil. Whisk until the discard is dissolved.
¾ cups + 1 ½ tablespoons (200 grams) warm water, ½ cup (100 grams) sourdough starter discard, 1 tablespoon (14 grams) extra virgin olive oil
Add the flour and salt to the bowl. Mix everything together until a smooth, sticky dough forms.
2 ½ cups (300 grams) all-purpose flour, 2 teaspoons (8 grams) kosher salt
Cover the bowl and let the dough proof for about 2 hours at room temperature (70-75℉), or until it doubles in size.
Transfer the dough to a lightly floured surface. Divide it into 8 equal-sized pieces (about 76 grams each). Shape each piece into a ball by bringing the edges to the center and rolling seam-side-down on the counter to seal them.
Cover and let the dough balls rest for 20 minutes to relax the gluten.
Roll out each dough ball into a 6-inch wide circle that's about ⅛-inch thick. It's helpful to roll out most or all of the pitas before cooking.
Preheat a cast iron or stainless steel skillet over medium heat. Do not add oil to the skillet.
Once the skillet is hot, place the first pita in it. Cook for about 30 seconds, or until bubbles start forming on the surface and it begins to puff up. Then, flip and cook for another 30 seconds on the other side. Repeat the cooking process with the remaining pitas.
Note: The first one or two pita are usually paler and don't puff up quite as nicely. This happens when the skillet isn't quite up to the right temperature yet. Cook a few and adjust the temperature of your burner accordingly.
Transfer the cooked pitas to a wire rack to cool. Serve them with hummus, sandwich fillings, or enjoy them on their own!