In a large bowl, whisk together water, yeast, sugar, whole wheat flour, and 1⁄4 cup of the all-purpose flour. Let the mixture rest for 15 minutes. Mix with a spoon, then add yogurt and stir to combine.
On a lightly floured surface, knead the dough for 2 minutes, then let it rest for 10 minutes covered with plastic. Knead it again for another minute and put into an oiled bowl. Cover the bowl with plastic and leave to rise on the counter for 2 hours. (If you’re making this a day in advance, put the dough in the fridge before the 2-hour rise, and refrigerate overnight. Pull the dough from the refrigerator 2 hours before you plan to cook the flatbreads.)
Roll out the dough into 4 to 6 balls and dust with flour. Cover and leave to rise for 1 hour.
Use your hands or a rolling pin to stretch or roll the dough until it’s about 1⁄4-inch thick. Heat a pan on medium high, add a nub of butter, and cook flatbreads on both sides until golden brown, about 5 minutes total. Alternatively, you can place the dough right onto an oiled grill, or onto the floor of a pizza oven. Flip the flatbreads halfway through cooking to finish cooking on the other side.
While the flatbreads are still warm, brush them with fresh olive oil and sprinkle with flaky salt and toasted sesame seeds.