This bread is easy, all you need is a bit of time (at least 24 hours). I plan to try additional toppings - but the za'atar was delicious!
3 1/2 cups (19 1/4 oz) bread flour
2 1/2 teaspoons instant or rapid-rise yeast
2 1/2 tsp sugar
1 1/3 cups (10 2/3 oz) ice water
1/2 cup plus 2 tablespoons (4 1/3 oz) extra virgin olive oil
2 tsp salt
1/3 cup za'atar
​coarse sea salt
In the bowl of a food processor, pulse the flour, yeast and sugar together until combined, about 5 pulses. With the processor running, slowly add ice water through the feed tube until the dough is just combined and no dry flour remains, about 10 seconds. 

Let dough rest for 10 minutes.

With the processor running, slowly add 2 tablespoons oil and the salt. Process until the dough forms a satiny sticky ball that clears the sides of the bowl, about 1 minute. 

Transfer dough to a lightly floured surface and knead by hand until smooth, about 30 seconds, and form a smooth round ball. Place dough ball seam side down in a lightly greased container, cover tightly and refrigerate for at least 24 hours (or up to three days). 

Remove dough from refrigerator and let sit for 1 hour to come to room temperature. Coat a rimmed half sheet pan with 2 tablespoons olive oil. Gently press down on teh dough to deflate it. Transfer dough to the sheet pan, and gently press the dough out to uniform thickness (without tearing the dough). (The dough may not fit into all the corners of the pan quite yet.) Cover loosely with greased plastic wrap and let dough rest for 1 hour.

Adjust oven rack to BOTTOM middle position and heat to 375°. Combine the remaining oil and za'atar.

Using your fingertips, gently press dough into the corners of the pan. Using a spoon or a pastry brush, spread the oil/spice mixture all over the bread. Then, using your fingertips, gently dimple all over the surface of the dough. 

Bake until the bottom crust is evenly browned and edges crisp, 20 to 25 minutes, rotating halfway through baking. Let bread cool in the sheet for 10 minutes, then transfer to a cutting board. Sprinkle with salt to taste, slice and serve warm.
Source: America's Test Kitchen Bread Illustrated

Notes:
  • I did the last rise in my oven on proof setting (100°) and it rose nicely.
  • I found it really hard to spread the oil/za'atar after dimpling, so here I'm recommending spreading the topping, then dimpling. Yes, dirty hands are part of the fun :)
  • The recipe is a little unclear how much oil is meant to be combined with the za'atar; I suspect is is 1/2 cup minus the 2 tbsp spread on the sheet pan. I ended up using a little less than 1/2 cup and foud it was a little too much. 
  • I want to try a garlic version of this!