Add 1 egg, the sugar, salt and oil to the milk. Sift 2 cups of flour (leave 1 cup aside for kneading), add the baking soda, stir and add the milk mixture.
Knead a soft dough, while adding some flour (the dough must not stick to your hands but it shouldn't be too hard either because your Khachapuri will become tough).
Cover the dough with a towel and leave it to loosen up. Grate the cheese on a coarse grater, add 1 egg and knead - your filling is now ready.
Form the dough into a roll. Cut the roll into 9 parts. Shape a thin pita from each piece of dough. Put 1-2 tbsp of filling in the middle of each pita.
Bring the edges in toward the middle and stick them together. Roll out the resulting ball once again but not too thinly and don't press too hard. If desired, you can smear with yolk.
Bake the Khachapuri in a preheated oven until golden. Smear the ready Khachapuri generously with butter.