Preheat the oven to 350°F (175°C).
Line two baking sheets with parchment paper or lightly grease them with cooking spray.
Using kitchen scissors or a sharp knife, cut each pita bread into halves, then quarters, and finally into small triangle-shaped chips.
Place the pita triangles in a large mixing bowl.
Drizzle with olive oil.
Sprinkle the za'atar seasoning, salt, and black pepper (or cayenne) over the pita pieces.
Toss well until every piece is evenly coated.
Arrange the pita chips in a single layer across the prepared baking sheets without overlapping.
Bake for 10–12 minutes, or until the chips are golden brown and crisp.
Remove from the oven and allow the Baked Pita Chips with Za'atar to cool for a few minutes before serving.