Adjaruli Khachapuri

Bread:

1. In a small bowl, sprinkle the yeast over the lukewarm water. Stir briefly and allow to sit at room temperature until frothy, about 10 minutes.
2. In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour, sugar, and salt.
3. Mix in the water with frothy yeast and oil until a soft dough forms.
4. Knead on a lightly floured surface just until elastic and smooth. Place in a large bowl, cover, and allow to rest at room temperature until doubled, 1-2 hours.
5. On a lightly floured surface, roll the risen dough into a smooth ball, then cover and set aside at room temperature for another 30 minutes.

To assemble:

1. Preheat oven to 425˚F (220˚C). Line a large baking sheet with parchment.
2. In a large bowl, combine the shredded cheese and splash of milk (just enough to bring it all together).
3. On a lightly floured surface, roll the dough in a large oval about 14 inches (35.5 centimeters) long.
4. Spread half of the cheese mixture across the bread, leaving about 1 inch (2.5 centimeters) clear around the edges.
5. Roll up each of the edges a couple of times, enclosing a little of the cheese and creating a boat shape.
6. Pinch together and lightly twist the dough at the two ends to seal.
7. Transfer the bread to the prepared baking sheet.
8. Fill the center of the bread with the remaining cheese, then brush the edges with the beaten egg.
9. Bake in the preheated oven until the bread is golden and the cheese is melted, about 20-25 minutes.
10. Use a spoon to gently press down some of the cheese in the center of the bread and carefully add the egg yolk.
11. Continue to bake for another 2-4 minutes, just enough to heat the egg but it should still be runny.
12. Remove the khachapuri from the oven and carefully rub some of the butter around the edges of the bread, then place a slice or two of butter next to the egg yolk in the center.
13. Use a fork to mix the cheese with the butter and egg, then serve immediately.