Step 1Heat the oven to 400 degrees. Cut the green calyxes off the eggplants. Cut each eggplant in half lengthwise. Using a sharp paring knife, cut a box in the center of each eggplant half, coming about half an inch from the sides and cutting down to within half an inch of the bottom. Using a large spoon, pry the center free. It should come out fairly cleanly, but use the spoon to scrape any excess eggplant from the inside of the box. Place the halves cut side down on a baking sheet lined with paper towel. Cover the excess eggplant flesh with plastic wrap and set aside. Repeat, cleaning all the eggplants.
Step 2Chop one of the onions and combine it with one-fourth cup of the olive oil in a large skillet. Place the skillet over medium-high heat and cook until the onion softens, about 5 minutes. Add the minced garlic and reduce the heat to low. Continue cooking an additional 3 minutes.
Step 3While the onions and garlic are cooking, bone the shoulder chops, then trim the fat and cut the meat into pieces about the size of the tip of your little finger. You'll have about three-fourths of a pound. When the garlic is fragrant, add the meat to the skillet and cook over medium heat, stirring occasionally, until the lamb has lost its raw color, about 5 minutes. The lamb will not brown.
Step 4Chop the reserved eggplant flesh into pieces about the same size as the meat. Add it to the skillet and cook until the eggplant has softened completely, about 5 to 7 minutes.
Step 5Add 1 cup of the crushed tomatoes and cook until the color dulls a little, about 5 minutes. Stir in the pine nuts and parsley and remove from the heat. Taste and correct the seasoning.
Step 6With the remaining tablespoon of oil, grease a large baking dish (about a 14-inch oval). Cut the remaining onion in quarters and then slice thinly. Put the slices in the bottom of the baking dish and pour the remaining crushed tomato over it. Arrange the eggplant halves in the baking dish. They should fit tightly. Spoon the lamb mixture into the eggplant boxes, dividing evenly.
Step 7Cover the baking dish with aluminum foil and bake 15 minutes, then remove the foil and spoon some of the tomatoes from the bottom of the baking dish over the eggplants, paying particular attention to the exposed cut sides. Re-cover with aluminum foil and bake, spooning the tomato mixture over the eggplants twice more at 15-minute intervals.
Step 8After 45 minutes total cooking time, bake just 10 more minutes, then spoon tomatoes for the last time and scatter the grated cheese generously over the top of the eggplants. Bake uncovered until the cheese is lightly browned, 5 to 10 minutes. Remove from the oven and cool at least 10 minutes before serving.