Wash the eggplants, and then peel about 4 stripes down their sides (as pictured). Cut as close to the stem as possible to remove them (discard the stems), and then slice about 1/4 inch off the top. Save these, so you can use them as caps.
Core the eggplants with a zucchini corer. Sprinkle their insides evenly with the 3/4 teaspoon salt and set them open-side-down to drain. Drain for 30 minutes to an hour.
Preheat the oven to 400° F.
While you're waiting on the eggplants, prepare the filling: Heat a large skillet over medium heat for about 2 minutes. Add 1 tablespoon of the butter, followed by the pine nuts, and cook, stirring constantly, for about 5 minutes, until the pine nuts are lightly toasted. Remove to a medium bowl.
Wipe down the skillet and add 1 tablespoon olive oil, followed by the onions. Stir occasionally, until they soften, about 7 minutes. Remove to the pine nut bowl.
Crack a window, turn on your exhaust, turn the heat up to high, and wait 1 minute. Add 1/2 teaspoon olive oil to the skillet, swirl to coat, and immediately add half of the diced meat and 1/2 teaspoon of salt. Cook, stirring every minute or two, until it browns (about 5 to 6 minutes). Remove the first batch of meat to a bowl, and immediately add another 1/2 teaspoon of oil and the rest of the meat. Let it cook until it browns, which will take a little less time than the first batch (about 3 to 4 minutes). Remove to the bowl and let it cool for 2 minutes, then stir in the parsley and allspice. Remove the skillet from heat, and don't bother washing it yet (unless the bits stuck to it have turned from brown to black).
Stuff the eggplants with as much of the meat mixture as will fit. Take the reserved caps and squeeze them into the tops so they stay in place. **
Combine the leftover meat mixture with the diced tomatoes and return to the skillet. Simmer for about 2 minutes over medium heat, just to meld the flavors.
Pour half of the tomato-meat sauce into the bottom of a casserole dish. Arrange the stuffed eggplants on theirs sides. Pour the other half of the tomato-meat sauce over the tops, pushing big chunks of meat and tomato off the tops, so they fall down the sides. Drizzle the top with 1 tablespoon of olive oil, or go over it with cooking spray. Cover everything with foil, and bake for 30 minutes. Uncover and cook for another 10 minutes. Sprinkle with parsley (optional) and serve.