Sift about 200 g of flour into a deep bowl, add dry yeast, sugar and salt. Mix the dry mixture.
Then add warm milk and vegetable oil - mix everything well.The last step is to add 20 grams of soft butter.We knead by hand a soft dough, not overloaded with flour, but at the same time quietly lagging behind the hands.Leave the dough in a warm place for an hour.
Grate all the cheese on a coarse grater.Add the egg, sour cream and remaining butter. The filling should be airy and loose. We leave some of them separately.
Divide the risen dough into 4 equal parts.Alternately, we roll out each blank into a thin circle. We spread the cheese mass on the tortillas, and then make a "big dumpling" out of them, lift the edges of the dough and fasten it in the center, forming a "bag" with the filling.
We roll out our "dumpling" from two sides, giving it the appearance of a thin tortilla so that the cheese is inside the tortilla.
Grease the dough with a shaken raw egg on top and sprinkle with the remaining cheese mass.
Bake khachapuri in Megrelian style in an oven heated to 220 degrees for about 20 minutes until golden brown.