In a small bowl, combine the warm water with the yeast. Set aside and let sit in a warm spot until foamy and frothy, about 10 minutes.

In a large bowl, combine 2 1/2 cups flour, salt, olive oil and water/yeast mixture. Stir with a wooden spoon (or with a paddle attachment of an electric mixer) until the dough comes together. Transfer to a lightly floured work surface and knead by hand, kneading in the remaining 1/2 cup of flour until the dough becomes smooth and somewhat soft, about 5 to 8 minutes. You could also just knead on high in an electric mixer.

Place the dough in a lightly oiled bowl, turning over to coat both sides, and cover loosely with plastic wrap and a damp kitchen towel. Set in a warm spot until doubled in size, about 1 to 2 hours.

Punch the dough down, and transfer to a floured work surface. Cut into 8 even portions. Place on a baking sheet and cover with a kitchen towel. Meanwhile, preheat oven to 450 degrees F along with a baking stone set in the center.

OR heat a large cast iron skillet over medium-high heat.

Working with one piece of dough at a time, roll out into a 8 to 9-inch circle on a well floured work surface. Transfer the dough onto the hot baking stone or cast iron skillet. Cook until fully puffed up, about 1 to 2 minutes. Transfer to a plate and cover with a kitchen towel. Continue cooking the rest in the same manner, making sure to cover them with the kitchen towel each time. Once all of the pitas are cooked and somewhat cooled, charr on an open flame and then cut into wedges.

To prepare the cheese, drain and then pat dry with a few paper towels. Drizzle the feta with 1 tablespoon olive oil and then set under the broiler until golden brown and crispy, about 2 to 4 minutes.

Pour the remaining olive oil onto a platter or serving dish, and top with the sliced chili pepper and oregano leaves. Set the cheese on top of the oil and then season with a bit of salt and pepper. Serve with the warmed pita.