Step 1

Dissolve sugar in lukewarm water, add the yeast and set aside until foamy, about 5-10 minutes.

Step 2

Combine flour and salt in a large mixing bowl. Make a well and add eggs, matsoni, oil, and water and yeast mixture. Stir until a shaggy dough forms.

Step 3

Turn dough out onto a lightly floured surface and knead until cohesive, tacky and glossy, about 5-10 minutes

Step 4

Transfer dough to a lightly oiled bowl, cover, and let rest at room temperature until doubled in size, about 1.5 - 2 hours.

Step 5

Preheat oven to 220°C (425°F) and place a baking sheet on the centre rack of the oven.

Step 6

Punch down dough, divide in two, and, working one by one, roll each piece out on a lightly floured surface until it reaches about 5 centimetres thick and about 20 centimetres in diameter.

Step 7

Place cheese in lines at the top and bottom of the dough circle, leaving about 2 centimetres of dough along the edge. Roll each side of dough to the middle of the circle until you have two parallel cheese-filled cylinders.

Step 8

Pinch both ends of the dough together, joining the cylinders at both ends and gently pull them apart in the middle, making an eye-shape and a wide middle. Fill middle with remaining cheese, taking care not to pack it down

Step 9

Brush each khachapuri with one egg beaten with a tablespoon of water. Transfer to baking sheet in oven and bake until lightly golden brown, about 8 minutes. Pull the khachapuris out and add one egg yolk to the centre of each bread, baking a total of 2 more minutes, or until dark golden brown and cheese is molten.

Step 10

Transfer to a wire rack and top with a pat of butter. Serve immediately.