Let the pizza dough proof for about 1 hour at room temperature.
In a bowl add 1 1/2 cups shredded mozzarella cheese, 3/4 cup crumbled feta cheese, 1/2 cup grated Parmesan, and 1 cup ricotta cheese. Then mix it all together.
Place your pizza dough onto a floured surface and divide it in half. Now take one of those halves, shape it into a ball and roll it out to about 9 inches in diameter. Then repeat this with the other half of the dough.
Place both doughs onto a baking sheet lined with parchment paper and begin filling the center of each khachapuri with the cheese mixture.
Now roll up the side of each khachapuri and twist the ends. We’re going for a boat like shape here. Cover the cheese boats with a kitchen towel and proof for about 30 minutes.
Once the khachapuri is done proofing, remove the towel and brush the dough with egg wash.
Bake the khachapuri at 350 degrees Fahrenheit for 20 minutes.
Then make a well in the center of each cheese boat, crack in egg on the middle and add 1 tbsp of unsalted butter to each khachapuri.
Bake for an additional 5 minutes and enjoy the khachapuri while it’s warm.