INSTRUCTIONS:
Step 1
Make the dough
Mix flour, sugar, salt, and yeast in bowl in foot processor and or mix into well incorporated
Add water and mix for 15-30 seconds until well formed
Transfer to lightly floured surface and knead gently
Make into well formed smooth ball
Refrigerate for at least one day to allow dough to rise
Step 2
Heat oven to 450 degrees (or 425, if using a convection oven). Line a half sheet tray with parchment paper; set aside. On a lightly floured surface, stretch and roll dough into a circle, ¼-inch thick, 10 to 12 inches across. Brush off excess flour, then lay the dough on the sheet tray. Using your fingers, roll, press and pinch two opposite sides of the circle a few inches into the center, building sides up, then press and pinch the narrow ends together to form two points. Continue to pinch and press the sides to create a raised rim and form the dough into an oval boat with an eye-like shape. Let rest in a warm place while you prepare the filling.
Step 3
In a medium bowl, combine mozzarella, goat cheese and feta with 3 tablespoons water. Stir with a fork until the mixture is thoroughly blended. Scrape the cheese mixture into the center of the dough boat, spreading it into an even layer.
Step 4
Bake khachapuri until the crust begins to brown and the cheese is melted, about 15 minutes. Remove pan from oven, leaving oven on. Brush sides of khachapuri generously with melted butter. Return khachapuri to the oven for an additional 5 minutes until the crust is extra crisp and the cheese just starts to brown around the edges.
Step 5
Using a spoon, make a shallow, 2-inch-wide well in the center of the cheese. Add the egg yolk and cold butter, and serve immediately. To serve, hold down one pointed end of the hot khachapuri with a fork; using another fork, quickly stir the egg and butter (if using) into the cheese mixture until it’s smooth and stretchy. Rip pieces of the bread boat off to dip in the cheese while it’s still hot.
NOTE: Don't worry about the raw egg. It cooks with the butter on top of the bread and makes a salty savory custard!