Combine the cheese in a small bowl.
Divide the dough into two pieces.
Working on top of a lightly floured piece of parchment, gently stretch each piece of dough into 12 inch-long ovals.
Spread a quarter of cheese mixture in the middle of each bread, leaving 1/2 inch border all the way around.
Pinch the ends, rolling tight to form points on either side. Add the remaining cheese evenly onto each bread.
Brush the bread with a light coating of olive oil. Transfer the Khachapuri on the parchment onto a baking sheet and allow to rise for 15 minutes.
Heat oven to 450°F.
You can make the breads one at a time.
Bake for 14 minutes, or until golden and the cheese is bubbly.
Remove cheese bread from oven, and gently add an egg yolk to the middle of the bread.
Bake for another 2 minutes.
Remove from oven and immediately add 1 tbsp cubed butter around the yolk.
Serve by swirling the yolk, cheese and butter all together. This dish is best eaten while still hot. Recipe inspired by TheNosher.