Pour the dosa batter into the middle of the unheated pan and spread the batter using a 3 oz. spoodle with a flat bottom, spreading the batter in a circle to completely and evenly cover the pan surface.
Sprinkle the za’atar seasoning on the dosa batter and season with salt and pepper while the batter is wet. Turn the heat to high and cook.
Spray the top of the dosa gently with pan spray to prevent cracking as it cooks.
Crack the eggs into separate souffle cups. Whisk the poaching water and drop in the eggs, one at a time.
Top the dosa with the shredded mozzarella as it cooks. The total cooking process should take 3 minutes, finishing as the dosa pulls away from the pan and turns browns on the edges.