Add warm water, yeast and sugar into the bowel of a stand mixer and mix well. Allow mixture to stand for about five minutes or until the yeast mixture begins to form small bubbles.
While waiting for the yeast mixture to activate, sift 3 cups of all-purpose flour.
Add sea salt and olive oil to yeast mixture. Using the dough hook attachment of your stand mixer and turn on to medium speed. Begin to slowly add 2 1/2 cups of the sifted all-purpose flour to the bowl until you have a smooth dough that easily pulls away from the bowl.
Remove the dough from the mixing bowl and form a large ball. Spread 2 tsp of extra virgin olive oil to a glass or metal bowl that is large enough for the dough to double in size. Place the dough into the bowl, cover with a clean, thick kitchen towel and set in a warm place to rise for 1 1/2 to 2 hours. (We use our oven but be careful no one turns it on!)
Once the dough has risen, turn it over onto a floured surface and divide the dough into 8 even sections. We weigh each piece to ensure they are as equal as possible. Form 8 small dough balls. Let them sit for about 5 minutes.
Sprinkle a small amount of flour onto your work surface, and with a rolling pin, roll each ball out into a 7-8 inch round that is about 1/4 inch thick.
Warm a cast iron skillet under medium heat. Brush some extra virgin olive oil to the bottom of the skillet and place one of the rolled out pitas onto the skillet to cook. After 30 seconds, the pita will begin to form bubbles on top.
Flip the pita bread to the other side and cook for 2 minutes, watching carefully not to burn. Turn once more and cook for about 1 minute, watching carefully not to burn the pita.
Place cooked pitas on a rack to cool.
Repeat until all dough balls are cooked.