Pour the water, extra virgin olive oil, and sourdough starter into a mixing bowl. Mix well with a dough whisk until the sourdough starter dissolves in the water.
Add the whole wheat flour, all purpose flour, sea salt and knead until the dough comes together. Use your hand to knead inside your bowl for a minute or two until there are no dry spots remaining in the dough.
Knead the dough by hand for about 15 to 20 minutes until it becomes soft and elastic.
Form a ball with the dough, place it in a greased bowl, cover with plastic lid or wrap, and let it ferment in a warm place for at least 4 hours or until it doubles in size.
Stretch and fold the dough, divide it into 8 equal pieces, form balls, and let them rest for about 10 minutes covered with a kitchen towel.
Preheat the oven to 450 degrees Fahrenheit (230 degrees celsius) with a pizza steel, cast iron pan, or cookie sheet inside.
Use a rolling pin to stretch the dough into thin circles, around 6 inches in diameter.
Place the dough on a baking sheet, cover, and bake until fully inflated and cooked. Flip and cook for another 1-2 minutes.
Transfer the pita breads to a cooling rack and let them cool for 10 minutes before serving.
