In a bowl mix 1/2 cup olive oil and 2 tablespoon za’tar.
In another bowl mix the cheddar and mozzarella cheese.
In a bowl add flour, 2 tablespoon sugar and yeast. Mix well. Set aside

In a small pan add milk and yogurt. Heat it up slightly. Add to the flour mix along with the oil and salt. Mix well with a spatula. Sprinkle some flour and knead. The flour should be soft and sticky. Keep kneading sprinkling a little flour for 10 minutes. Oil your palm and knead. Put it in a bowl brushing some oil on dough and let it rest for 2 hours or so to double in size.

Remove air from the dough. If the dough is sticky that is normal. Make 10 equal size balls and roll in thin rounds. Keep it aside for 15 minutes.
Heat a tawa or pan. Take one rolled dough and cook for 30 to 40 seconds on one side. Flip and add za’tar oil on the other side and cook until the bottom side when lifted is golden brown. Fold and remove in a serving plate. Repeat and add cheese instead of za’tar mix. You have 2 different manakish. One with cheese and other with za’tar. Enjoy