01 -
Heat the butter and milk together in a small saucepan or in the microwave until the butter melts. Place the sugar (or malt powder), coriander, and salt in a large bowl, and pour the hot milk over it, stirring to dissolve. Cool to lukewarm, about 100°F to 110°F.
02 -
Add the yeast and flour to the milk mixture, stirring until a shaggy mass forms. Cover with plastic wrap or a reusable bowl cover and let rest for 10 minutes.
03 -
Knead the dough until smooth (8 to 10 minutes by hand, or 6 to 8 minutes at medium speed in a mixer). Add 1 to 2 tablespoons additional flour if the dough is too sticky. Place in a greased bowl, cover, and let rise for 1 to 1 1/2 hours, until it increases in size by at least one third.
04 -
Combine all filling ingredients in a large mixing bowl and beat to combine, or pulse everything together briefly with a food processor, leaving some bits of the cheese intact.
05 -
Line two baking sheets with parchment. Divide the risen dough into four equal pieces (about 150g each). Roll each piece into an oval shape about 10" long and 6" wide. Cover with greased plastic wrap and let rest for 15 minutes.
06 -
Spoon one quarter of the cheese mixture (about 119g) into the center of each oval and spread to within 1" of the edges. Pull the dough's edges up around the cheese, folding and twisting the ends to form a boat shape.
07 -
Cover the shaped khachapuri and let rise for 20 minutes, or until puffy but not doubled. Meanwhile, preheat the oven to 375°F with two racks toward the center.
08 -
Brush the exposed edges of the khachapuri with egg wash and bake for 15 to 20 minutes, until they feel set (they won't have started to brown nor will the filling be bubbly yet).
09 -
Remove from the oven and use the back of a spoon to make an indentation about 3" across in the filling of each khachapuri. Crack an egg into each, place a teaspoon of butter on top, and return to the oven.
10 -
Bake for an additional 8 to 10 minutes (for soft-set eggs), or 12 to 15 minutes (for firmer eggs). Remove from the oven and serve warm, garnishing with additional fresh herbs if desired.