Preheat the broiler. Place the eggplants on a foil-lined baking sheet and broil, turning once, until blackened and tender, about 20 minutes. Let cool slightly.
Meanwhile, chop 1/2 cup herbs. Mix with the lamb, breadcrumbs, pine nuts, 1 tablespoon olive oil, the garlic, egg, lemon zest, 1 teaspoon salt and a few grinds of pepper in a large bowl. Shape the mixture into 12 large meatballs and place on a plate.
Peel off the eggplant skin; discard. Transfer the flesh to a colander and let drain 5 minutes, then transfer to a food processor and pulse until chopped. Scrape into a bowl and stir in 2 tablespoons olive oil and the yogurt; season with salt and pepper.
Line the baking sheet with a clean sheet of foil. Arrange the meatballs on the pan and broil until golden brown and cooked through, 6 to 8 minutes, turning once halfway through.
Toss the pomegranate seeds, remaining 1 cup herbs and 2 teaspoons olive oil, and the lemon juice in a bowl; season with salt and pepper. Spoon the eggplant mash into shallow bowls and top with the meatballs and pomegranate mixture; serve with lemon wedges.