In small bowl, mix za’atar, sumac, salt and pepper; set aside.
Scoop out a quarter‐size hole in the center of each slice of bread. Heat 1⁄4 cup oil in a large skillet over medium heat until hot.
Arrange half of the bread slices in the skillet and brown about 1 minute on each side. Reduce the heat to low and crack one egg into the hole in each slice of bread. Sprinkle za’atar mixture evenly over each egg, cover and cook until eggs have reached your desired doneness (2 to 3 minutes).
If you like your yolk cooked really well, scoop up some oil from the bottom of the skillet and drizzle over each egg.
Using a spatula, transfer the toasts to a platter or serving plate and keep warm. Repeat with the remaining 1⁄4 oil and bread slices.