In a large mixing bowl, combine the 00 flour, baking powder, and salt. Stir to blend evenly.
Add Greek yogurt gradually, about ½ cup at a time, stirring until a dough begins to form. Shape into a ball.
Dust a work surface with flour and knead the dough for 3–5 minutes, until smooth and elastic. If the dough feels sticky, add 2–4 tbsp more 00 flour while kneading. Let the dough rest 15–30 minutes at room temperature.
Divide into 6 equal parts and roll each into a ball. Roll out into thin circles, 5–6 inches wide.
Heat a cast iron or heavy skillet over medium heat. Once hot, cook each round for about 1 minute per side until golden patches form.
Drizzle lightly with olive oil and continue flipping every 30 seconds for another 3–4 minutes, until puffed and golden brown.
Repeat with the remaining dough.
Serve warm — with oregano, tzatziki, or your favorite fillings.