Preheat oven to 475 degrees. Line 2 baking sheets with kitchen parchment and brush with the vegetable oil.

Divide the dough in half and roll one piece into a 12" round,1/4" thick, on a lightly floured surface. Allow the dough to relax if it's too elastic to roll out easily. Transfer it to one of the baking sheets, brush with olive oil, then sprinkle a few tablespoons of Za'atar on top. Repeat with second piece of dough. Bake until they brown and blister, about 8-10 minutes. Cut into wedges, slices, strips or break into random pieces.