Brown the lamb in a large frying pan over a medium heat. Add the onion and garlic and cook for 5 minutes, stirring often, until the onion is soft. Add the eggplant and stock and cook, stirring, for 5 minutes, until the eggplant is tender.
Stir in the tomatoes and half of the herbs. Season with salt and pepper and bring to a boil. Reduce to a simmer, cover, and cook for 20 minutes, or until the lamb is tender.
Preheat the oven to 350°F. Meanwhile, cook the orzo according to package directions, until al dente. Drain.
Beat together the yogurt and egg in a small bowl.
Stir the drained pasta into the lamb mixture and spoon into a large (7×11-inch) baking dish. Spread the yogurt mixture over the top and bake for about 20 minutes until piping hot. Sprinkle with the remaining mint and dill just before serving.