Soak very salty cheese in water for 2-5 hours at the beginning. Drain cheese in a colander. Break up with fingers and mix well in a baking bowl with eggs and (if cheese is very lean) a spoonful of oil. Divide quantity into 4 parts.
Make a dough not too firm with mazoni or salt, milk, eggs and flour. Divide the finished dough into 4 parts and roll out into thin patties. On each patty put a part of the filling form. Either pinch only the edges together to prevent the filling from spilling out, or close them completely.
Bake in a dry, heated, cast-iron skillet, seam side down, with the lid closed. When they are done on one side, flip to the other side and finish baking with the lid open.
You should adjust the size of the khachapuri to your frying pan. Bring to the table hot.
Tip: The higher the fat content in the yogurt, the more aromatic and creamy the result!