Heat oven to 500˚F.
Mix 6 ounces mozzarella or sulguni with feta, ricotta and 1 egg yolk. Set aside.
Divide dough in half, roll each into a 6x10–inch rectangle, and place on parchment-lined baking sheets.
Spread cheese mixture along long edges of each rectangle, leaving 1–2 inches dough uncovered at ends. Roll dough edges up around cheese to form stuffed crust, and press to seal. Gather cheese-free ends of dough and pinch together to create boat shape. If necessary, gently stretch dough to make wide, long oval in center. Fill centers with remaining shredded cheese. Bake until crusts are brown and cheese is bubbly, about 5–7 minutes.
Remove from oven. Working quickly, use 2 forks to blend 1 egg yolk and 1 tablespoon butter into melted cheese of each khachapuri. Serve immediately. Serves 4.
Baia’s Wine 2019 Tsolikouri (Imereti)
“Given the cheesy and buttery goodness of the Ajaruli khachapuri, I would look to an acidic white like a Tsitska or Tsolikouri,” says Jonathan Nelms, Supra’s owner. “There’s a brilliant young pair of sisters—Baia and Gvantsa Abuladze—who make this and several other wines in western Georgia that retain great acidity in the subtropical climate.”
Domaine Jean Vullien 2019 Jacquère (Savoie)
In the Savoie region of the French Alps, light, crisp and faintly floral white wines like this one made from the Jacquère grape are commonly matched up with cheese fondue. It would go equally well with the cheesiness of this khachapuri.