Preheat oven to 400 degrees. Heat 2 teaspoons oil in an ovenproof pot over medium heat. Cook onion, stirring often, until soft and lightly caramelized, 10 to 12 minutes. Add lamb, breaking it up with a wooden spoon. Season with 1 teaspoon salt and 1/4 teaspoon pepper. Cook until lamb is cooked through and no longer pink, 3 to 4 minutes. Add stock, rice, and currants. Bring to a simmer. Cover, and transfer to oven on lowest rack. Cook for 1 hour and 20 minutes.
Meanwhile, slice eggplants in half lengthwise; brush each cut side with 1/4 teaspoon oil. Roast, cut sides up, on a rimmed baking sheet on top oven rack until centers are soft and tops are browned, about 40 minutes. Let cool.
Gently scrape eggplant flesh into a large bowl, reserving skins. Stir in lamb-rice mixture, chopped herbs, and lemon zest. Divide stuffing among eggplant skins. Garnish with more herbs and lemon zest.