I usually make my bread dough using the processor but this is easily done by hand. Put all the ingredients for the dough into the processor bowl and knead together until everything comes together into a smooth and somewhat loose elastic dough thatu2019s just short of sticky.
Transfer the ball of dough to a well-oiled bowl, turning it so it is coated all over. Loosely cover and let it rise till double in volume, about 1 to 1 1/2 hours.
Place a pizza stone or a baking sheet on a rack in lower third of oven and preheat oven to 250C (500F).
Combine the cheeses in a bowl and set aside. Deflate the dough and divide it into two halves. Working with one piece at a time, roll it out to a rectangle about 10" long and 1/8" thick on a piece of lightly floured parchment. This makes it easier to transfer the dough to your baking sheet.
Roll the long sides in a bit curving them inwards at the ends and seal well (with a little water) or the edges will open up during baking. Then bring the edges close and pinch together on both ends to form a "boat" like shape. Again, make sure the ends are sealed well. Transfer the "boats" to the baking sheet, but if you're going to bake them directly on the pizza stone just omit this step.
Dock the centre “well” area and fill with half of the cheese mixture so it is a little higher than the edges of the dough “boat”. Repeat with the other half of dough and bake them for about 12 to 15 minutes until the Khachapuri are golden brown.
Take the breads out of the oven and gently crack an egg on each bread without breaking the yolk (or add the sliced tomatoes, pickled jalapeños and herbs like I did) and return them to the oven. Bake for another 3 to 4 minutes till the egg is set.
Take the Adjaruli Khachapuri out, and place a couple of cubes (2tbsp) butter on each. Serve them hot. It helps to wait for about 10 minutes before eating them so you don’t burn your mouth!