Step 1

In a small bowl, whisk together the water, yogurt and ¼ cup oil. In a large bowl, whisk together both flours, the yeast and ¾ teaspoon salt. Make a well in the center and pour the liquids into the well. Using a silicone spatula, gradually incorporate the dry ingredients into the wet; once combined, the mixture should form a shaggy dough.

Step 2

Dust the counter with all-purpose flour and turn the dough out onto it; reserve the bowl. Knead the dough until smooth and elastic, about 2 minutes, adding flour as needed to prevent sticking. Lightly coat the same bowl with oil, then return the dough to it. Cover with a clean kitchen towel and let rise at room temperature until the dough has doubled in bulk, 30 to 60 minutes.

Step 3

Meanwhile, cut eight 9-inch squares of kitchen parchment; set aside. In a small bowl, stir together the remaining ¼ cup oil, the za’atar, sumac, oregano and the remaining ¼ teaspoon salt; set aside.

Step 4

When the dough is ready, dust the counter with flour, then turn the dough onto the surface. Using a dough scraper or bench knife, divide the dough into 8 pieces, each about 87 grams (3 ounces). Form each portion into a taut ball, keeping the formed balls covered with the kitchen towel as you shape the rest. Set 1 ball on a lightly floured surface and, using a rolling pin, roll it into an 8-inch round about ⅛ inch thick, dusting with flour as needed. Lightly flour a parchment square and set the round on top. Repeat with the remaining dough balls, stacking the rounds on top of each other, with a parchment square between the layers.

Step 5

Heat a 10- to 12-inch cast-iron skillet over medium until water flicked onto the surface immediately sizzles and evaporates. Pick up a dough round by its parchment liner, invert it into the pan and peel off and discard the parchment. Cook until large bubbles form and the bottom is spottily browned, 1 to 2 minutes. Using tongs, flip the bread and cook until the second side is golden brown, about 1 minute. Transfer to a wire rack and brush the surface with the za’atar oil. Cook the remaining dough rounds in the same way and brush them with za’atar oil. Wipe out the pan if excess flour begins to build up and smoke, and adjust the heat as needed. Serve warm or room temperature.