Step 1 In a medium bowl, pour the boiling water over the bulgur and set aside until the water is completely absorbed and the bulgur has cooled to room temperature, about 1 hour. (This step can be done 1 day ahead. Cover loosely and set aside at cool room temperature.)
Step 2 In a small bowl, combine the lukewarm water, yeast and sugar. Set aside until the mixture is foamy, about 5 minutes.
Step 3Meanwhile, in a large bowl, whisk together both flours along with the salt. Add the yeast mixture and bulgur and stir until a dough forms. Transfer the dough to a very lightly floured surface and knead until smooth, about 5 minutes.
Step 4Brush a medium bowl with olive oil. Place the dough in the bowl and turn to coat lightly with olive oil. Cover the bowl with a clean dish towel and set aside in a warm, draft-free area until dough doubles in volume, about 1 hour. Punch the dough down and knead briefly. Divide the dough into 8 equal rounds, about 3 1/2 ounces each. (The dough can be made ahead of time. Wrap each dough round in plastic and refrigerate up to 3 days. Unwrap the dough as needed, giving it time to warm up before using.) Cover the rounds with plastic wrap and set aside until slightly puffy, about 45 minutes.
Step 5Heat a griddle or grill over medium-high heat. Combine the oil and garlic in a bowl. Roll a piece of dough out on a lightly floured surface to a 6- to 7-inch round. Brush each round with the garlic oil and place, oiled side down, on the griddle and brush the top with garlic oil. Cook until lightly browned on the bottom, about 3 minutes. Turn the flatbread and brush with garlic oil and sprinkle with za’atar, about 1 tablespoon. Cook until lightly browned on the bottom, about 2 minutes. Transfer to a cutting board. Cut into wedges and serve with labneh.