How to make
Dissolve the yeast in the slightly warmed milk and water. Add the sugar and stir.
Sift the flour on the kitchen counter and make a well in the middle. Pour in the yeast (don't wait for it to activate), the lightly beaten egg whites and the oil. Gradually knead a soft dough and transfer it into a greased bowl.
Cover it with cling film and leave it to rise for about an hour. Divide the finished dough into 5 parts (equal) and roll each one out into a round crust that is not very thin.
Sprinkle its entire surface with grated yellow cheese and roll up from two of its ends to get something like a boarder full of yellow cheese. Assemble the two open ends and you will have something like a boat shape. Inside, crumble the white cheese onto the yellow cheese.
Arrange the prepared khachapuri in a tray covered with baking paper, leaving a space between them. If they do not fit, use a second tray. Allow the khachapuri to rise a second time for 30-40 minutes.
Coat their boarders with beaten egg yolk and bake them in a preheated 340°F (170 degree) oven for 15-20 minutes. Take them out of the oven and crack 1 egg into each boat. Place them back in the oven.
Spread the Adjarian Khachapuri with Egg with a little butter and eat it immediately.