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Preheat the oven to 500°F, preferably with a baking steel or stone on the center rack.
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In a medium bowl, combine the flour, sugar, salt, and yeast.
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Add the water, then use a spatula or bowl scraper to mix and fold the dough until just combined.
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Cover the dough and let it rise in a warm spot for 30 to 40 minutes, until puffy, with small bubbles on the surface.
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Coat a metal 9" x 13" pan with 1 tablespoon of the olive oil.
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Transfer the dough into the prepared pan. Use a bowl scraper or oiled hands to flip the dough so that both sides are coated in oil. Drizzle the remaining 1 tablespoon oil over the dough, then use your fingertips to gently stretch the dough to the pan’s edges. If the dough resists, cover, and let the dough relax for 10 to 15 minutes before trying again.
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Dimple the surface of the dough, then sprinkle evenly and generously with za’atar.
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Lower the oven temperature to 450°F. Place the pan with the flatbread on the preheated baking steel, if using, and bake for 15 to 20 minutes or until golden brown. The bread will shrink away from the sides of the pan.
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Let cool slightly, then slice and serve warm.
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Storage information: Za’atar flatbread is best served fresh. Freeze slices for long-term storage and reheat, wrapped in foil, in an oven until warmed through.