Start kneading the dough. In a bowl, mix kefir, sunflower oil, salt (on the tip of a knife). Gradually add sifted flour to the mixture and knead the dough.
Form the flat cakes. Divide the resulting dough into 2 parts. Sprinkle the work surface with flour and roll each portion of dough with a rolling pin into a thin flat cake.
Heat a frying pan without adding oil and fry the flatbreads over medium heat on both sides until golden brown, about 1-2 minutes.
Fry the eggs. Transfer the flatbreads to a plate, return the frying pan to the heat, add vegetable oil and break the chicken eggs without stirring. Fry the eggs for 5-7 minutes over medium heat under the lid.
Place the eggs from the pan onto the flatbreads. Melt the butter in the pan, add salt and a pinch of pepper (black, allspice or cayenne).