Preheat oven to 350°F (175°C).

Cut the eggplants in half lengthwise and scoop out the flesh, leaving about ¼ inch intact.

In a large saucepan, heat olive oil over medium heat and sauté onions for about 4 minutes.

Add chopped eggplant flesh and cook until soft and lightly browned, then stir in garlic, salt, pepper, and oregano.

Incorporate tomatoes, tomato paste, and parsley, then simmer for 10-15 minutes.

Arrange eggplant halves cut side up in a baking dish, fill with the mixture, and top with breadcrumbs.

Pour hot water around the stuffed eggplants, cover with foil, and bake for 30-40 minutes until tender.

Uncover, sprinkle cheese on top, drizzle with olive oil, and bake for an additional 5-10 minutes until cheese melts.

Whisk together yogurt, buttermilk, garlic, and salt while eggplants bake, and refrigerate until serving.

Let the baked eggplants rest for 15 minutes before serving, then top with yogurt sauce, pomegranate seeds, and thyme.