Cut the eggplants in half lengthwise and remove the inside flesh to create boat-like shells. Chop the eggplant flesh, sprinkle with some salt and place in a colander for 30 minutes. Sprinkle inside of eggplant shell with some salt, turn them upside down on towels to drain. (During these 30 minutes, chop and prepare the other ingredients.)
Squeeze the chopped eggplant to remove excess water. Heat 1/3 cup of the olive oil in a large skillet. Add the chopped eggplant and saute until eggplant is browned. Add the tomatoes and, over high heat, cook the mixture until the liquid has evaporated. Add the bread crumbs, shrimp, garlic, olives, anchovies and capers and cook for a few minutes more for the flavors to come together. Season to taste with salt and pepper.
Preheat the oven to 375 degrees. Fill the eggplant shells with the mixture, set them in a baking sheet and drizzle remaining olive oil over the top. Bake for 1 hour. Serve hot, warm or chilled, sprinkled with parsley.