Combine flour, yeast, and salt in a standing mixer bowl fitted with a dough hook.

Add water and oil and mix with a rubber spatula until a rough dough forms.

Knead on medium speed for about 7 minutes until the dough comes together but is still a little ragged.

Transfer the dough to a lightly oiled bowl or dough-rising container, cover with plastic wrap, and refrigerate overnight until doubled in volume.

One hour before baking, remove the dough from the refrigerator.

Turn it onto a lightly floured counter top and divide it into 2 equal pieces for large flatbreads or 6 equal pieces for small ones.

Shape the dough pieces into loose rounds, sprinkle with flour, and drape with plastic wrap.

Let stand until puffy and almost doubled in volume, about 1 hour.

While the dough rounds are proofing, place a baking stone on the middle rack of the oven and preheat the oven to 400°F.

Line a baker's peel with parchment paper.

Stretch the larger dough pieces into 8-inch circles or press the smaller ones into 3-inch circles using your hands.

Place the dough circles on the parchment-lined peel.

Press your fingertips into the dough rounds to create little dimples.

Brush the rounds liberally with olive oil and sprinkle with za'atar.

Slide the dough, still on the parchment, onto the hot baking stone and bake until lightly browned, about 10 minutes for large breads, 7 minutes for small ones.

Slide the breads, still on the parchment, onto a wire rack to cool slightly.

Serve warm, or cool completely and serve at room temperature. Mana'eesh are best eaten on the day they are baked.

For longer storage, freeze in a zipper-lock plastic bag for up to 1 month.

To defrost, place on the counter top for 15 to 30 minutes, and reheat in the oven at 350°F for 5 minutes before serving.