Whisk the dry ingredients. In a mixing bowl, combine flour, baking powder, and salt until evenly distributed.
Add yogurt and oil. Spoon in the Greek yogurt and add 1–2 teaspoons olive oil. Mix with a spoon until shaggy, then switch to your hands to bring it together.
Knead briefly. Turn the dough onto a lightly floured surface. Knead for 1–2 minutes until smooth and slightly tacky but not sticky.
If it’s sticky, dust in a tablespoon of flour at a time. If it’s dry, add a teaspoon of yogurt.
Rest the dough (optional but helpful). Cover and let sit 5–10 minutes. This relaxes the gluten and makes rolling easier.
Divide and shape. Cut into 6 equal pieces for small flatbreads or 4 for larger wraps.
Roll each piece into a ball.
Roll it out. Dust your surface and rolling pin. Roll each ball into a round or oval, about 1/8-inch thick (2–3 mm). Don’t stress about perfect circles.
Preheat the pan. Heat a large cast-iron or nonstick skillet over medium to medium-high.
Lightly brush with olive oil.
Cook the flatbread. Lay a rolled dough onto the hot pan. Cook 1–2 minutes until bubbles form and the underside has golden spots. Flip and cook another 1–2 minutes.
Adjust heat to prevent burning.
Keep warm. Stack cooked flatbreads in a clean kitchen towel to stay soft while you finish the batch.
Serve. Brush with a touch of olive oil, sprinkle with sea salt or herbs, and enjoy warm.