In a mixing bowl add in ½ cup warm water, sugar, and active dry yeast. Set it aside for 10 minutes until yeast is foaming and activated.
Once yeast is activated add in flour, salt, and remaining water. In a stand mixer with dough hooks on low speed OR by hand using a spoon/spatula start mixing dough. Slowly add in oil until fully combined into dough. Once oil is mixed in fold by hand a few times to ensure everything is mixed well. In a floured bowl place dough and cover with kitchen towel. Allow to rise in a warm area for 1 hour.
Once dough has doubled in size, divide into 12 equals pieces using a Dough Cutter. Roll each piece into a ball between the palm of your hands and place onto a parchment paper lined baking tray. Cover with kitchen towel and allow to rise one more time for 30-45 minutes.
While the dough rises for the second time mix together toppings. Mix Za'atar and olive oil in one bowl. In another bowl, crumble feta cheese and add in mozarella cheese, pressing with spoon to help fully crush feta.
Preheat oven to 425°F.
Once dough balls have risen on a floured surface roll out thinly to 6in in diameter. Transfer to parchment paper lined tray and then put on toppings leaving a thin border on the edge of dough. You will end up with 6 za'atar and 6 cheese manaeesh.
Bake for 10-12 minutes or until the bottom is golden brown and cheese is bubbling.