Start kneading the dough. Mix milk, sugar and yeast in a bowl and leave for 10 minutes. Beat the egg with a fork or whisk and add to the milk mixture, add salt. Gradually add flour, knead a soft dough that does not stick to your hands. Then roll the dough into a ball, place it in a bowl and let it rise for 50-60 minutes, covering it with a damp towel. Leave it in a warm, dry place without drafts, the dough should double in volume.
Form a flat cake. Knead the dough and divide it into four equal parts. Roll each part into a round layer, not thin. Place some of the filling in the center. Lift all the edges up and connect them well "in a bag". Carefully roll into a flat cake of the desired diameter. Leave for 5-7 minutes so that the dough rises a little.
Fry the flatbreads. Heat the vegetable oil in a frying pan and fry each yeast flatbread on both sides until golden brown. After frying the flatbread on one side, turn it over and make a hole for the steam to escape by piercing the flatbreads in several places with a fork.
Remove the finished flatbreads from the heat and place them on a paper towel to remove excess fat.