In a medium bowl, whisk together the flour, salt, and baking powder to evenly distribute the leavening agents. Add the Greek yogurt and stir with a wooden spoon or spatula until a shaggy dough begins to form. The yogurt adds moisture and tang while creating a tender crumb. If the dough feels too dry and crumbly, add yogurt 1 tablespoon at a time; if it's too sticky to handle, dust in a bit more flour. Mix until you have a cohesive, slightly tacky dough with no dry flour streaks.

Shape the dough into a rough ball and place it in the same bowl or on a clean surface. Let it rest for 30 minutes at room temperature without covering it. This resting period allows the flour to fully hydrate and gluten to relax, making the dough much easier to shape and resulting in a more tender flatbread. I find that this short rest is the key to getting soft, pliable dough that doesn't spring back when you roll it.

After resting, turn the dough out onto a lightly floured work surface and knead gently for just a few turns to bring it back together. Divide the dough into 4 equal pieces and roll each piece into a ball. Working with one ball at a time, use a rolling pin or your hands to roll it into a thin, even circle about 1/8-inch thick, roughly 6-8 inches in diameter. If the dough shrinks back, let it rest for a minute before continuing to roll. Lightly flour as needed to prevent sticking, and stack the rolled flatbreads with parchment paper between them so they don't stick together.

Heat a large cast-iron skillet or non-stick pan over medium-high heat and lightly brush or drizzle the olive oil across the surface. Once the oil shimmers and the pan is hot, carefully lay one flatbread into the skillet. Cook for 2-3 minutes without moving it, allowing it to develop golden-brown spots and light charring on the bottom. Flip the flatbread and cook the other side for another 2-3 minutes until it too has golden-brown spots and slight char marks. I love the slight char because it adds depth of flavor and creates a pleasant texture contrast. Transfer the cooked flatbread to a plate and repeat with the remaining three portions, adding a touch more oil if needed between batches.