Make dough: Sprinkle yeast and sugar over warmed milk; stir to dissolve. Set aside to proof for five to 10 minutes – mixture will become bubbly and foamy.

Combine: Meanwhile, place two cups flour and salt in a large mixing bowl (or in stand mixer with dough hook). Whisk to blend; then make a well in the center, pushing flour against sides of bowl. Add proofed yeast mixture and butter to the well. Mix flour slowly until a dough forms and comes away from sides of bowl.

Knead until dough is a soft and elastic pliable ball, adding in remaining quarter cup flour as needed if dough is too sticky. Cover bowl with a towel and allow to rise until dough is doubled in bulk, about an hour.

Filling: Preheat oven to 425 degrees Fahrenheit. Combine mozzarella, feta, cottage cheese, and one egg in a mixing bowl; stir together until well mixed. Set aside.

Shape: Divide dough in half. Place one half of dough on a lightly floured piece of parchment paper. Using a floured rolling pin, roll out into an oblong shape about a quarter inch thick. Mound half the cheese mixture in the middle of the dough, pressing and spreading into an even layer, leaving a border of plain dough.

Fold in the long sides of dough to slightly cover the cheese on each side. Twist and seal the ends together on each side to form a boat shape. Brush outer edges of dough with egg wash. Slide parchment onto a baking sheet. Repeat with remaining dough and cheese.

Bake: Bake for 10 to 14 minutes, or until dough is lightly browned. Remove from oven; using the back of a spoon, make an indentation in the center of the cheese. Crack two eggs into two separate glasses and pour each one into each indentation. Return to oven; bake for an additional five minutes or until egg is half-way set but still runny.

Remove from oven and add one to two tablespoons butter to the cheesy center of the khachapuri. Serve immediately.

To eat: Use a fork to beat up the egg and butter into the cheese filling. Tear off pieces of the bread’s crust and dip into the cheesy center.