About 1 hour before baking, heat the oven to 500°F with a baking steel or stone on the upper-middle rack. In a small bowl, stir together the oil, sesame seeds and za'atar. Lightly dust a baking peel, inverted baking sheet or rimless cookie sheet with semolina.

Transfer one portion of the shaped dough to the peel and, if needed, reshape into a 6-by-12-inch oval. Spoon half of the oil mixture evenly over the entire surface of the dough. Slide the dough onto the baking steel and bake until the edges are golden brown, 7 to 9 minutes.

Using the peel, transfer the baked flatbread to a wire rack. Let cool for about 10 minutes. Meanwhile, top and bake the second portion of dough in the same way. Serve warm.