Drizzle some oil in a frying pan and turn on heat to medium.
In a small bowl, mix together olive oil and za'aatar mix.
When pan is hot, crack in the two eggs.
After about a minute, use a spoon to sprinkle the za'atar mixture and then the cheese evenly on top of the eggs.
Allow egg whites to fully cook, or to your preferred doneness.
Serve with flatbread and a small salad.