Preheat the grill to high (for marking and toasting the pita bread).
Combine all of the za’atar spice ingredients in a clean coffee grinder or food processor.
Pulse the grinder a few times to grind up the sesame seeds, just a few seconds is fine. There, you made the za’atar! That was easy.
Now that the grill is hot, turn the heat down to low and place the pita bread on the grill.
Once you smell the pita toasting, flip them over and toast on the other side. All we are looking for here are some tasty grill marks and warming up the bread.
Remove the pita from the grill.
Brush the pita with the olive oil, sprinkle with the za’atar and cut into strips.
Serve with extra za’atar spice for a nice and easy appetizer while you grill the rest of your dinner.