Since there are so few ingredients here, you'll get the best resutls by using high-quality ingredients.
1. Preheat oven to 425 degrees. Grease two large baking sheets (or you can bake flatbreads one at a time). Combine the za'atar and olive oil in a small bowl.
2. Cut the pizza dough in half and roll out each half on a floured surface to a 15-inch oval. Transfer to greased baking sheet(s).
3a. If you want a crisp flatbread, bake the plain dough for 8 minutes before spreading with za'atar mixture. Spread half the mixture on the par-baked dough, leaving a little bit of an edge. Bake for an additional 5 to 10 minutes, until crisp and golden.
3b. If you want a chewy, pull-apart flatbread, spread the za'atar on the raw dough, leaving an edge, and bake for about 15 minutes until edges start to turn golden.
4. Cut into wedges or break apart and serve warm or at room temperature.