Georgian cheese is hard to find, so I combined two cheeses to give an approximate flavour of the real thing. This dish quickly became a test-kitchen favourite.
3/4 cup yogurt
3 tbsp butter, melted
1/2 tsp salt
1 3/4 cup all-purpose flour, plus extra for dusting
1/4 tsp baking soda
1 cup (4 oz) fresh mozzarella
3/4 cup (3 oz) feta, crumbled
1 egg, lightly beaten
Stir yogurt with egg, butter and salt. Combine flour and baking soda.
Gradually add flour mixture to yogurt mixture, stirring with a wooden spoon until all flour has been added.
Scrape dough onto a lightly floured surface. Knead for 6 to 8 minutes, or until smooth and elastic, dusting with more flour as needed. Place dough in a clean bowl. Cover with plastic wrap and refrigerate for 20 minutes.
Tear fresh mozzarella into small pieces and combine with feta. Mix in 2 tbsp beaten egg. Reserve.
Preheat oven to 425 F. Line a baking sheet with parchment paper.
Divide dough in half. Roll and stretch one portion into a 10-inch circle. Scoop half the cheese filling into the centre of the dough. Flatten cheese into a 5-inch circle. Pull edges of dough over the filling, pleating in 2-inch sections and pinching to seal. Dough should not overlap in the centre – it should just come together. Lift onto baking sheet. Repeat with remaining dough and filling.
Brush the tops of the pies with remaining beaten egg. Bake for 15 to 20 minutes, or until golden and cooked through. Remove to a rack to cool.