Step 1

Preheat the oven to 375°F (190°C). Line 3 baking sheets with parchment paper.

Step 2

Make the khachapuri filling: In a large bowl, combine the mozzarella, ricotta, feta, egg, parsley, salt, and pepper. Mix with a fork until well combined, then use the back of the fork to mash into a chunky, but uniform, paste. Transfer half of the filling to a separate large bowl.

Step 3

Make the roasted tomato and garlic filling: On a prepared baking sheet, combine the tomatoes, shallots, and garlic. Drizzle with the olive oil and season with the ajika, if using, and salt. Toss until the tomatoes are well coated.

Step 4

Roast for 12–15 minutes, until the tomatoes and shallot have softened. Remove from the oven and let cool for 15 minutes.

Step 5

Make the spring greens filling: Bring a medium saucepan of salted water to a simmer over medium-high heat. Blanch the asparagus for 2 minutes, until bright green and barely tender. Add the peas for the last 30 seconds of cooking to defrost. Use a slotted spoon to transfer the vegetables to a paper towel-lined plate to drain.

Step 6

Add the blanched vegetables and the scallions, dill, and coriander to a bowl of khachapuri filling. Stir to combine.

Step 7

Add the roasted tomato mixture to the remaining bowl of khachapuri filling and stir to combine.

Step 8

Shape the dough: On a lightly floured surface, divide each portion of pizza dough in half and shape into balls. On a floured surface, shape and stretch one of the balls using your hands and a rolling pin into a 12-inch-long oval or boat shape, about 6 inches across at its widest point. The outer edges of the dough should be slightly thicker than the center, similar to pizza. Transfer the boat to a prepared baking sheet and repeat with the remaining dough, fitting two boats per pan.

Step 9

Divide the tomato-garlic filling between two of the dough boats, spreading to 1 inch from the edges. Fold the edges of the dough over the filling, overlapping the corners and twisting the ends to seal and create boat shapes.

Step 10

Divide the spring greens filling between the remaining two dough portions and repeat to shape the boats.

Step 11

Brush the edges of the boates with the beaten egg yolk. Sprinkle the edges of the spring greens boats with the toasted sesame seeds and the edges of the roasted tomato boats with the dried minced garlic.

Step 12

Bake the khachapuri for 20 minutes, until the filling is set and the edges are beginning to brown.

Step 13

Remove the khachapuri from the oven and use the back of a spoon to create a small divot in the filling at the center of each of the khachapuri. Crack 1 egg into each divot and top each with 1 tablespoon of butter. Return to the oven for 8–10 minutes, until the egg whites are set and the yolks are runny. (For a more set egg, cook for 3–5 minutes more, or until done to your liking.)

Step 14

Garnish with more herbs, if desired. Serve immediately.

Step 15

Enjoy!