Pulse flour, yeast, and sugar in food processor until
combined, about 5 pulses. With processor running, slowly
add ice water and process until dough is just combined and
no dry flour remains, about 10 seconds. Let dough rest for
10 minutes.
Add 2 tablespoons oil and salt to dough and process
until dough forms satiny, sticky ball that clears sides of
bowl, 30 to 60 seconds. Transfer dough to lightly floured
counter and knead by hand to form smooth, round ball,
about 30 seconds. Place dough seam side down in lightly
greased large bowl or container, cover tightly with plastic
wrap, and refrigerate for at least 24 hours or up to 3 days.
Remove dough from refrigerator and let sit at room
temperature for 1 hour. Coat rimmed baking sheet with
2 tablespoons oil. Gently press down on dough to deflate
any large gas pockets. Transfer dough to prepared sheet
and, using your fingertips, press out to uniform thickness,
taking care not to tear dough. (Dough may not fit snugly
into corners.) Cover loosely with greased plastic and let
dough rest for 1 hour.
Adjust oven rack to lower-middle position and heat
oven to 375 degrees. Using your fingertips, gently press
dough into corners of sheet and dimple entire surface.
Combine remaining 6 tablespoons oil and za'atar in
bowl. Using back of spoon, spread oil mixture in even layer
on entire surface of dough to edge.
Bake until bottom crust is evenly browned and edges
Coarse sea salt
are crisp, 20 to 25 minutes, rotating sheet halfway through
baking. Let bread cool in sheet for 10 minutes, then transfer
to cutting board with spatula. Sprinkle with sea salt, slice,
and serve warm.