In a stand mixer fitted with the hook attachment, mix the flour, water, yeast, sugar and salt until it comes together in a shaggy mixture, about 1 minute. Add the olive oil and continue to mix until the dough becomes soft and smooth and lightly sticky without leaving any dough on your fingers, about 5 more minutes.
Lift the dough from the bowl, lightly oil the bowl and return the dough back to the oiled bowl. Cover the dough in the bowl with a slightly damp kitchen towel and set aside at room temperature until the dough has puffed and risen to double its volume, about 90 minutes.
Remove the dough and divide into 24 pieces, about 30 grams each, and shape into round balls. Let sit in an oiled tray covered until doubled in volume, about 30 more minutes.
Make the Cheese Mixture
In a large bowl, combine the mozzarella cheese, feta cheese, parsley and black pepper. Set aside in the fridge until ready to use.
Assemble & Bake
Preheat the oven to 400ºF. Line two baking sheets with parchment paper and lightly sprinkle flour on top.
Divide the dough into the two trays with 12 balls each and keep them covered while you work.
Use your hands to flatten the dough in a circular shape, about 5-inches wide. Place 2 heaping tablespoons of the cheese mixture inside each circle. Pinch the dough from two opposite sides up in the shape of a boat. Press the cheese mixture down.
Bake for 14-16 minutes until the tops are golden brown and the cheese is melted. 2-3 minutes before they finish baking, you can use a spoon to push down any cheese that starts to ooze out.
Notes
Storage: Allow the homemade cheese fatayer to cool completely to room temperature. Then, transfer them to an airtight container or a resealable zip-top bag and keep them in the refrigerator for up to 4 days.Tips:Proper dough kneading. Make sure your dough is smooth, elastic, and doesn't stick to your hands or the bowl. If it does, knead for a few more minutes. Working the dough on a flat surface like a countertop can be helpful.Grease the bowl. After kneading the dough, lightly oil the bowl and transfer the dough back into it to prevent it from sticking later.Keep the dough covered. To prevent the dough from drying out, keep it covered with a damp kitchen towel any time you're waiting for it to rise or when you need to be working on other components.Push down the cheese. Two or 3 minutes before the cheese fatayer finishes baking, you can use a spoon to push down any cheese that starts to ooze out.