Combine all the ingredients for the dough in a large mixing bowl or the bowl of the stand mixer. Mix and knead until a soft, pliable dough forms. Remove the dough into a lightly greased bowl, cover and set aside to rise for 1 hour.
Dough should be almost doubled. Punch down lightly and divide it into 6 equal pieces. Roll out each piece into a thin oval. At this point, dough might not stretch all the way, so try as much as you can, but don't fret too much. Place the rolled out pizzas on 2 baking sheets, cover and set aside to rest.
Preheat the oven to 450°F. Place a pizza stone in the oven. If you don't have one, then put a baking sheet to preheat.
In a small bowl, combine tomato paste, drained chopped tomatoes, salt and pepper to taste.
In another bowl, mix the cheeses, parsley, salt, pepper and beaten egg (if using). Mix well to combine.
Try and stretch out the dough as thin as possible. Spread the tomato paste evenly over the lahmacun, taking it almost to the edges. Top it with the cheese mix.
Slide the pizzas on the heated pizza store or baking sheet and bake for 7~9 minutes or until the base is cooked, but still soft and the cheese is bubbling.
Remove from the oven and roll each one up while still hot and enjoy right away.