In a large mixing bowl, add the Greek yogurt, flour, baking powder, salt, and minced garlic. Using a fork or silicone spatula, mix gently until the ingredients begin to come together and form a rough dough.
If the dough looks dry or crumbly, add warm water one tablespoon at a time, mixing after each addition. Stop as soon as the dough becomes soft and slightly tacky, holding together without sticking heavily to your hands.
Once combined, cover the bowl and let the dough rest for 5–10 minutes. This resting time allows the flour to hydrate fully and helps relax the dough, which keeps the flatbreads soft instead of tough.
Transfer the rested dough onto a lightly floured surface and divide it into 6 equal portions. Roll each portion into a smooth ball, then gently flatten it into a round about ¼-inch thick, using your hands or a rolling pin.
Place a nonstick skillet over medium heat and allow it to preheat fully. Do not add oil at this stage, as a dry pan helps the flatbreads cook evenly without becoming greasy.
Carefully place one flatbread into the hot skillet and cook for 2–3 minutes, until bubbles form on the surface and light golden spots appear underneath.
Flip the flatbread and cook the second side for another 2 minutes, until cooked through and still soft. Adjust the heat slightly if the bread browns too quickly.
Remove the cooked flatbread from the skillet and immediately brush lightly with olive oil. Stack the flatbreads and cover loosely with a clean kitchen towel to keep them warm and flexible while you cook the remaining ones.