Mix together the Za'atar and the olive oil in a bowl and set aside.
Mix together the mozzarella cheese and feta cheese and set aside.
Once the dough is ready, separate into 10 equal-sized balls. Using a floured rolling pin and a floured surface, flatten each dough ball to a very thin medium sized flatbread. The dough will rise slightly in the oven so it's important to make them thin
Transfer the dough rounds to a floured baking sheet. You may need to use 2-3 baking sheets to fit them all, or wait for some to bake then add the rest
Spread the Za'atar mixture on 5 of the manakish and make sure to cover the entire surface, leaving a ¼ inch border
Spread the cheese mixture on the remaining 5 of manakish, leaving a ¼ inch border. Sprinkle with the nigella seeds
Place the baking sheets in the oven on the bottom rack and bake for 12-15 minutes until the bottom is lightly golden. You can bake more than one sheet at one time, by placing one on the bottom rack and one on the middle rack. Once the bottom rack manakish are cooked, then switch the middle rack sheet pan to the bottom for a few more minutes until cooked through
For the cheese manakish, you can broil the top for just a few minutes to lightly brown the cheese. Keep an eye when you're doing this as it happens quickly
Remove baked manakish and place in a platter and cover with a towl or plastic bag to keep them soft until serving
Serve them with fresh vegetables like tomato, cucumber, mint, and olives