Heat olive oil in a saucepan set over medium. When oil shimmers, add onion, red pepper, garlic, za’tar, salt, and tomato paste and mix thoroughly. Sauté for 10 minutes, until vegetable are softened and the mixture is very fragrant.
Stir in tomatoes and cook for another 10 minutes, until tomatoes are breaking down and saucy.
Create four wells in the sauce, and carefully crack one egg into each well, taking care to not break the yolks. Cover and reduce heat to medium-low. Simmer for about 10 minutes, until whites are set but yolks are still runny.
Top with parsley. Serve with thick plain yogurt, rice, or crusty bread.