Warm the water to around 100 degrees and stir in the yeast
Add 2 3/4 cups of flour to a mixing bowl and make a depression in the flour
Add the yeast water, milk, oil and a raw egg.
You can add 1 teaspoon of sugar if you want your bread to have a golden color.
Mix the ingredients from the middle of the bowl until all the flour is mixed
The dough should be formed into a soft ball
Cover the bowl with plastic wrap and leave in a warm place for two hours to rise.
Preheat oven to 450 degrees
Add 1/2 cup of flour and knead the dough until it is soft and smooth
separate the dough into 2 pieces
on a floured surface roll out one piece of the dough into a circle about 11 "
Place the combination of seasoned cheese in the middle
Gather up the edges of the circle enclosing the cheese.
Flip over and roll out again to about a 9" diameter disc.
Transfer the khachapuri to a cookie sheet lined with parchment paper or a warm pizza stone
Repeat with the second part of the dough of freeze for later use.
Mix the egg yolk and water in a cup and brush the dough with the egg wash.
Bake for 18-20 minutes until golden brown.
Let cool for a few minutes and serve warm.