Eggplant Lasagna (Lasagne alle Melanzane)

Instructions

1. Slice the eggplant lengthwise into 1/4-inch thick slices (skin on or off, as desired). Layer the eggplant slices with salt and place them in a colander set into a large bowl. Weigh down the eggplant slices with a plate with a heavy object on top, such as a can of tomatoes or a heavy pot. Let sit for an hour. Rinse and pat dry very well. Fry in a half-inch of oil in a large skillet until golden on each side (adding extra oil as necessary). Drain well on paper towels and pat each slice with a paper towel to remove all excess oil.
2. Meanwhile, prepare the sauce. If using fresh tomatoes, proceed as follows. Core and cut the tomatoes in half. Squeeze out some of the seeds and juices and place the tomatoes in a large stockpot. Add water to about half the height of the tomatoes. Bring to a boil and wilt the tomatoes, stirring gently for 2-4 minutes until they look soft enough to place through a food mill with a fine disc. Drain the tomatoes well in a colander and puree them in a food mill which will remove the skins and any leftover seeds. You should have about 1 1/2 liters/quarts of tomato puree. 
3. To prepare the sauce with either canned tomatoes or the fresh tomato puree, heat the extra virgin olive oil in a large stockpot. Gently cook the onion until translucent and beginning to get tender, adding a pinch of salt as you put it in the pan. Next, add the garlic and cook gently for a few minutes until it starts smelling sweet. (If using a whole clove vs. minced, you may remove it if desired after it begins to get golden, or keep it in the sauce as it cooks and remove it at the end.) Add the jarred tomato puree and the hand-crushed tomatoes or the fresh tomato puree. Make sure to rinse out the jar and can with some water and add it to the pot. Don't waste any tomatoes! Season with salt and bring to a simmer. Cook until you have a nice thick sauce, about 1-1 1/2 hours. At the end of cooking, adjust the seasoning and add the basil, tearing the leaves by hand before you throw them into the pot. You should have about 3 cups of sauce. 
4. Next, make the pasta dough. Combine the two flours in a bowl after you have measured them. Place the flours on a clean work surface and form a well in the center by creating a circular wall of flour with enough space in the center to hold your liquid. Crack the egg into the well and start beating it with a fork, adding the flour bit by bit in a circular motion from the surrounding wall of flour to create a smooth dough that is moist, yet firm, and not sticky. Add water as necessary, little by little until the dough comes together. Once you’ve incorporated all of the flour into the eggs and water, gently knead the dough until it’s very smooth, pliable and doesn’t stick to your hands. Add flour as necessary to achieve the right consistency. It should take about 10-15 minutes. Let the dough rest, wrapped in plastic wrap for at least 30 minutes to an hour. (Or, place the dough on a plate and cover tightly with a bowl, making sure no air is getting in.)
5. While your dough rests, prep the filling ingredients and put a large pot of water on to the boil. Preheat the oven to 350 F/180 C.
6. Next, roll out your dough. If you know how to do it by hand with a rolling pin, roll it out until thin but not too thin (about 1/2 mm). If using a pasta machine, divide the dough into 4 pieces, covering those not in use. Flatten each piece, sprinkle lightly with flour, and run it through the #1 setting 2-3 times, folding over each time, add a little flour as necessary so that it doesn't stick. Next, run the pieces through the pasta machine, narrowing the setting each time, without folding over. Handle with care and roll out until about 1/2 mm thick. (This doesn't have to be super delicate.) Proceed with the other pieces and let rest about 10 minutes. Cut the pieces as necessary if they get too long to work with. Once they've sat and become less sticky, cut them into 5-6-inch lengths, so they will fit into your pan.
7. Set a large bowl of ice water next to your stove and get some tongs and a skimmer ready to help you quickly blanch the pasta. Line a large sheet tray with a kitchen towel. Have several clean kitchen towels ready to make layers of blanched pasta.
8. Take 4 pieces of lasagna at a time and place in the boiling water. Stir delicately and take them out immediately once they float to the top, using the skimmer and tongs. This should take about 15 seconds. Take them out and place in the ice water, stirring to keep them from sticking. Place all of the dried and blanched dough on your sheet pan and layer between towels. Do this with all of the dough. Make sure the pasta is not touching or it will stick. Set aside.
9. With this amount of dough, you should have enough pasta to make 6 layers of lasagna in a 9x9-inch/22x22 cm baking dish (mine is 2 1/2-inches/6 cm tall). Divide your filling ingredients into 5 so that you have an even amount for each layer. Set aside your 4 prettiest pieces of eggplant for the top. To assemble the lasagna, place a thin layer of sauce at the bottom of your baking dish.  Next, add a layer of eggplant. Then add a layer of pasta, 1/5th of the ham, 1/5 of the egg, and 1/5th of the scamorza and mozzarella cheeses, and top with Parmigiano-Reggiano. Add about  1/3 cup (heaping) of sauce on top and proceed with the next 4 layers in the same manner. Once you have used up your ham, eggs, and mozzarella and scamorza cheeses, add a layer of Parmigiano-Reggiano cheese, another layer of sauce and eggplant, then top with a last layer of pasta and the rest of your sauce, spreading it evenly. Top with a generous layer of Parmigiano-Reggiano cheese and place your last pieces of eggplant on top.
10. Bake, on a sheet pan to catch any drippings for approximately 45 minutes until bubbling and golden on top. If you like the top extra crunchy at the corners, you can very briefly and carefully place the lasagna under the broiler, taking care not to burn it! For the best results, let the lasagna sit a minimum of 15 minutes, preferably 25-30 minutes to let it set.