Place the yeast, warm water, and 1 cup of flour into the bowl of a mixer. Whisk together by hand and let it stand 15 to 20 minutes until the mixture is bubbly.
Add 1½ tablespoons olive oil, 1¾ teaspoon salt, and the rest of the flour into the mixture. Use the dough hook attachment and mix at low speed, until the dough is soft and just slightly sticky. If the dough is sticking to the sides of the bowl too much, add a little more flour, but no more than another ¼ cup.
Continue to mix/knead the dough on low speed for about 5 minutes. It should all combine together nicely and be stretchy and smooth.
Place the dough onto a floured work surface and form into a ball, tucking under to create a smooth surface.
Wipe the inside of a bowl with olive oil and place the dough ball inside. Cover the bowl with clear wrap sprayed with cooking spray and let the dough rest until it has doubled in size, about 2 hours.
Remove the dough from the bowl and place it onto a floured work surface. Lightly pat the dough into a flat rectangle shape about ½ inch thick. Use a knife to cut the dough into 8 pieces.
Form each piece into a small round ball by tucking the ends underneath a few times to make it nice and tight and smooth. Place each ball on a surface you can cover, I used a baking sheet with a silicone mat.
Cover the balls with lightly oiled plastic wrap and let them rest for 30 minutes.
Sprinkle a small amount of flour on your work surface and gently pat each dough ball flat with your fingers, forming a flat round disc about ¼ inch thick.
Brush a cast-iron skillet with olive oil and place it over medium-high heat. Place the dough round into the hot skillet and cook until bread begins to puff up and the bottom has brown spots, about 1-2 minutes. Flip and cook for 1-2 more minutes. Flip again onto each side for 30 more seconds each. Your pitas will start to bubble and fill with air (some more than others). Once evenly cooked on both sides, remove the pita from the skillet and place it on a plate for cooling.
Brush a little more olive oil in the skillet when needed and repeat cooking the rest of the dough rounds. Watch your heat as you are cooking, if the oil starts smoking or the pitas burn, turn down the heat and wait a few minutes before continuing to cook the rest of the pitas.