Preheat the oven to 375 degrees F.
Put the eggplant in a colander and sprinkle with salt. Let it drain for 30 minutes, then rinse, drain and pat dry and chop.
Cut the top third of peppers off horizontally, seed and reserve tops. Season the peppers with salt and pepper, to taste, and put them in a large bowl. Drizzle them with a little extra-virgin olive oil, and arrange them upright in an oiled roasting dish.
Heat the 1/4 cup of extra-virgin olive oil, in small pan over medium heat. Add the anchovies, if using, and let them melt into the olive oil. Stir in the garlic and rosemary and swirl for 1 to 2 minutes. Transfer the oil mixture to a mixing bowl and add the eggplant, potatoes, tomatoes, onions, olives, lamb and cheese. Toss to combine and fill the peppers, slightly overstuffing them. Set the tops in place and roast for1 hour. Cool and store for a make-ahead meal.
Reheat in a hot oven by adding a little chicken stock or water to the baking dish for moisture. Cover the baking dish with foil and bake for 20 minutes. Remove the foil and bake until hot and cooked through, about 10 more minutes. Serve 2 peppers per adult portion.