For the dough, combine 220ml warm (43C) water with the yeast and 1tsp of the sugar in a small bowl. Stir together and leave to rest for 5-7 minutes until foamy.
In a large bowl or stand mixer, whisk together the bread flour, salt and remaining 1tsp sugar. Add the milk, yeast mixture and oil to the dry ingredients.
Keeping the dough in the bowl, use the basic kneading technique: gently press it with the heel of your palm, pushing it away from you, then draw it back towards you with the inner surface of your fingers. Repeat for around 4-5 minutes, periodically rotating the dough by 45 degrees, until it is elastic and no longer sticky.
If using a stand mixer, attach the dough hook and mix on medium speed for 4-5 minutes. Cover the dough with cling film and allow to rest for 20 minutes.
Transfer the rested dough to a lightly floured work surface. Knead for 4-5 minutes until smooth. Shape into a ball and return to the bowl. Cover with cling film, then rest at room temperature for 50-60 minutes until almost doubled in size.
Line a baking sheet with baking paper. Transfer the dough to a lightly floured work surface and, using a knife or scraper, divide into four. Round each piece into a ball, transfer tothe baking sheet and cover with a clean tea towel. Rest at room temperature for 15-20 minutes.
For the filling, combine all the cheeses in a medium bowl and set aside.
Cut four square pieces of baking paper, each 30x30cm approx. On a floured work surface, roll a piece of dough into a 20x30cm oval and transfer to a piece of baking paper.
Leaving a 2.5cm border of dough on all sides, arrange one- third of the cheese mixture in the middle, in two rows along the longer sides of the oval. Roll the edges of the dough up over the cheese. Twist the smaller ends to form the khachapuri shape (like a small canoe). Add the remaining two-thirds of the cheese mixture to the centre of the dough and spread evenly.
Carefully transfer the baking paper on to a baking sheet and gently stretch the pointed ends of the oval to lengthen the khachapuri. Cover with a clean tea towel. Repeat to make the other three khachapuri, placing two on each of two baking sheets and leaving some space between them. Cover with a clean tea towel and leave to rise for 15-20 minutes.
Preheat the oven to 200C/180C F/Gas 6.
For the egg wash, beat the egg with the oil and brush over the outsides of the dough, then sprinkle the sesame seeds over.
Bake for 17-20 minutes until golden brown. Make a well in the centre of each khachapuri and crack an egg inside it, holding back half of the egg white in the shell – adding it all would cause it to cover the whole top. (Freeze the excess whites to use in another recipe.)
Return to the oven and bake for 2-3 minutes or until the egg white is cooked to your liking.
Add a slice of butter, some dill and a sprinkle of red pepper flakes and serve hot.
Recipes and photographs taken from Turkuaz Kitchen by Betül Tunç, photography by Betül Tunç (Square Peg, £25)
