In a large bowl, add water, sugar and yeast.

Let bloom until foamy and fragrant, about 10 minutes.

Add flour, olive oil, and salt to bowl and stir with wooden spoon until a soft, springy dough forms.

Transfer dough to well greased bowl and let rise in a warm area for 1 hour.

Preheat pizza stone in oven at 500 degrees (dont add stone to a hot oven, let it come to temperature in the oven so it doesn't explode.)

Generously flour a counter surface.

Punch down dough, and divide into two round balls.

Roll out one ball onto floured surface into a large disc, about 1/4" thick.

Add 1/4 cheese mixture to the center of the dough.

Roll the sides to form a boat shape around the dough.

Add another 1/4 cheese to the middle and place into oven.

Bake 30 minutes, or until cheese is bubbly and crust is a golden brown.

Top with fresh egg and pats of butter when removing from oven.

Repeat with second disc for second Khachapuri.

Serve and enjoy!