Over medium-high heat, warm a nonstick skillet. Add the olive oil and turn the heat to medium. Tilt the pan around to spread the oil, and watch for it to shimmer.
Carefully slide the eggs in the heated oil. Season with Kosher salt and the za'atar. Cook for about 2 to 3 minutes over medium heat, spooning some of the olive oil on top, until the whites are cooked the edges crisp up and the yolk is cooked to your liking (if you like, you can cover the pan for a few seconds to help it).
Serve immediately with warmed pita bread or your favorite crusty bread!
I like my eggs swimming in good EVOO, so I typically use more. But you can use more or less olive oil to your liking.
Add ons: I like adding a few chopped cherry tomatoes and sometimes a bit of feta. You can add those as soon as you season your eggs in step #3.
How long to fry your egg? It will take about 2 to 2 ½ minutes for runny yolk and 3 minutes for medium yolk. If you like to fry your eggs until the yolk hardens, you'll want to cover the skillet for a couple minutes and watch until the yolk is cooked to your liking.