Put the all-purpose flour, whole wheat flour, salt, sugar, and baking powder in a large bowl and whisk to blend everything well. Make a well in the center of the bowl and add the yogurt. Mix the flour into the yogurt a little bit at a time, using your hands or a rubber spatula to blend. If the dough seems dry, add another small spoonful of yogurt.
Once the flour is mostly combined with the yogurt, transfer the dough onto a lightly floured surface. Gently knead until the dough is smooth, about 30 seconds. Divide the dough into 4 to 6 equal portions, depending on your intended use. Using a rolling pin and your hands, shape each portion into a round, approximately ⅛ inch thick. Don't worry if the shapes aren’t perfectly round.
Heat a dry cast-iron skillet or griddle over high heat until it's very hot. Add the flatbreads, one or two at a time, depending on the size of your pan, and cook for about 1 minute on each side, until they puff up slightly and develop a light brown color with some charred spots. It's better to overcook the flatbreads slightly than to undercook them, as undercooking will leave them doughy and dense. If the flatbreads char too quickly before cooking through, lower the heat slightly. Wipe the pan between batches to remove any burnt flour.
Allow the flatbreads to cool on a wire rack. For the best flavor and texture, enjoy them within a few hours of cooking. If not serving immediately, store them in an airtight container until ready to use.
