Set oven to 400°F. Divide dough into four 6 oz portions. Roll into balls and allow to rest at room temperature for 15 minutes.
For each flatbread, flatten dough ball out slightly. Place 1/4 cup of feta cheese in the center and pinch dough around it to encase it. Dust work surface lightly with flour. Roll feta stuffed dough into a rough circle that is about 1/4" thick.
Use 1 tablespoon extra virgin olive oil to coat both sides of the flatbread. Lay flat on a parchment lined sheet tray. Sprinkle with 1 tablespoon of Za'atar seasoning. Use finger tips to create rows of dimples across the dough's surface. Bake until golden brown.
Allow to cool slightly then slice into wedges. Serve warm.
This flatbread could also be used as a cheese stuffed pita pocket for sandwiches.
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