Preheat Oven: Preheat the oven to 450°F (230°C). Line two baking sheets with parchment paper.

Prepare the Cheese Filling: In a bowl, combine feta, gouda/spicy cheddar, and provolone cheeses. Mix in 1 beaten egg and season with salt and pepper.

Shape the Dough: Divide the pizza dough in half. On a lightly floured surface, roll each dough piece into a rough oval shape (about 10 inches long). Transfer each dough to the prepared baking sheets. Spoon the cheese mixture evenly into the center of each dough round, leaving a 1-inch border. If using, arrange lemon slices over the cheese. Fold the edges of the dough over the cheese to form a “boat.”

Prepare the Dough for Baking: Brush the edges of each boat with the remaining beaten egg and sprinkle with sesame seeds.

Add Fresh Herbs: In a bowl, mix cilantro, parsley, dill, and garlic. Sprinkle the herb mixture over each bread boat.

Bake the Khachapuri: Bake for 20 minutes, or until the crust is golden and the cheese is melting. Remove from the oven and crack an egg yolk into the center of each boat. Return to the oven and bake for another 3-5 minutes, or until the egg yolk is just barely set.

Make the Honey Butter: While the Khachapuri is baking, prepare the honey butter by mixing the butter, honey, smoked paprika, red harissa (if using), and chili flakes in a small saucepan or bowl. Warm gently to combine.

Finish the Dish: Remove the Khachapuri from the oven and top with the honey butter. Stir the butter and egg yolk into the cheese. This will help finish cooking the egg. Serve immediately and enjoy!