To make this version of khachapuri you need to skewer the cheese and wrap the dough around it, instead of rolling them in a traditional way.
Flatten the dough and cut it into ribbons.
Cut the cheese into rectangles. Thickness of the cheese depends on how thick your khachapuri will be.
Skewer the cheese slices and wrap the dough ribbons around them, making sure that the cheese is covered entirely. Dab the dough with whipped egg and cook it over hot coals. If the latter are unavailable, you can bake the khachapuri in an oven.