Prepare the dough. Heat the water until it is slightly warm and dissolve the yeast in it. Pour 2.5 cups of flour into a deep bowl. The remaining half cup will be needed later. Pour the water into the flour. Add the egg and butter. Mix thoroughly. The dough should become smooth and soft. Cover with cling film and put in a warm place for 60 minutes.
While the dough is rising, prepare the cheese filling. In a bowl, mix the grated suluguni and Adyghe cheeses, egg, chopped herbs, garlic, pepper and butter. Leave on the table.
Prepare the khachapuri for baking. Add the remaining flour to the risen dough, knead and divide into 3 parts. Roll each part with a rolling pin into round flat cakes about 0.5 cm thick.
Place the filling in the center of each flatbread, dividing it into 3 equal parts. Wrap the filling in the dough, gathering it to the top. Compact with your hands, turn over and knead lightly. Roll out carefully with a rolling pin. Pierce with a fork in several places to allow air to escape during baking.
Place on a baking tray and place in an oven preheated to 180°C for 15 minutes.
Garnish the dish with assorted parsley, dill and cilantro before serving. Cilantro is a must! It is one of the foundations of Georgian cuisine.