Mix the dry ingredients. In a bowl, whisk flour, baking powder, and salt. If using self-rising flour, skip the baking powder and reduce the salt slightly if desired.
Add the yogurt and oil. Stir in Greek yogurt and olive oil with a spoon until shaggy bits form.
Switch to your hands and gently bring it together. It should be soft and slightly tacky, not sticky.
Knead briefly. Turn the dough onto a lightly floured surface. Knead for 1–2 minutes until smooth.
Avoid overworking; you just want it cohesive.
Rest the dough. Cover and let it sit for 5–10 minutes. This relaxes the gluten and makes rolling easier.
Divide and shape. Cut into 6–8 equal pieces. Roll each into a ball.
Keep covered with a towel so they don’t dry out.
Roll the flatbreads. On a floured surface, roll each ball into a circle or oval about 6–7 inches wide and 1/8 inch thick. Lightly dust as needed to prevent sticking.
Preheat the pan. Heat a dry skillet over medium to medium-high until hot. A drop of water should sizzle on contact.
Cook the first side. Lay a rolled dough in the skillet.
Cook 1–2 minutes until bubbles form and the underside has golden spots.
Flip and finish. Flip and cook another 1–2 minutes. If you like, brush with a little olive oil or melted butter and sprinkle with flaky salt.
Repeat and serve. Keep cooked flatbreads wrapped in a clean towel to stay warm and soft while you finish the rest. Serve right away.