In a stand mixer with the dough hook, mix the flour, sugar and yeast on low until combined, about 15 seconds. With the mixer running, gradually add the water and 2 tablespoons of oil.

Mix on low until the ingredients form a strong dough that clears the sides of the bowl, about 5 minutes. Cover the bowl with plastic wrap and let rest for 20 minutes.

Uncover the bowl, sprinkle the salt over the dough and mix on low until smooth and elastic, 5 to 7 minutes. Meanwhile, coat a large bowl with the remaining 1 tablespoon oil.

Transfer the dough to the prepared bowl. Dip your fingers into the oil pooled at the sides and dab the surface of the dough until completely coated. Using your hands, turn the dough over.

Tightly cover the bowl with plastic wrap and let rise at room temperature until the dough is doubled in bulk, about 1 hour. Transfer to the refrigerator and let rise for at least 24 or up to 48 hours.

Line a rimmed baking sheet with kitchen parchment and mist with cooking spray. Lightly flour the counter and turn out the dough. Using a chef’s knife or bench scraper, divide the dough into 4 even pieces, each about 8 ounces.

Shape each into a taut, smooth ball and place seam side down, evenly spaced, on the prepared baking sheet. Mist the tops of the dough with cooking spray, cover loosely with plastic wrap and refrigerate for 3 hours.

Heat the oven to 500°F with a baking steel or stone on the middle rack. Remove the dough from the refrigerator. Generously flour the counter and set the dough balls on top; reserve the baking sheet.

Dust the dough with flour and, using your fingertips, press each into a dimpled disk about 5½ inches wide and ½ inch thick. Return the dough to the baking sheet, evenly spacing the disks.

Mist the dough with cooking spray, cover with plastic wrap and let rise at room temperature until slightly puffy, about 1 hour.

Generously dust a baking peel with semolina. Flour your hands, then gently slide your fingers under one round of dough, lift and transfer to the prepared peel, placing the round near the edge so it will be easier to slide onto the baking steel.

Repeat with another round of dough, making sure the two don’t touch. Gently shake the peel back and forth to ensure the dough is not sticking, then, working quickly, open the oven and slide the rounds onto the steel.

Bake until the dough is puffed and golden brown, 7 to 10 minutes. Using the peel, transfer the breads to a wire rack. Lightly brush the tops with some of the za’atar oil. Bake the 2 remaining rounds in the same way. Serve the breads warm or at room temperature with the remaining za’atar oil for dipping.