Slice the eggplant into regular slices. For best results, slice vertically: when sliced in this direction, the eggplant fibers soak up less oil when fried. Cover with coarse salt (more than you think you need), and place in a colander in your sink, to sweat out their water or bitter juices (30 to 60 minutes). This is important because if they are too juicy inside, they’ll soak up oil like crazy when fried. In the meantime, heat 8 tbsp oil in a saucepan, add 1 clove garlic and the tomato, salt, and cook on low/medium heat for 10 minutes until thickened, stirring frequently with a wooden spoon. Cook the pasta according to instructions and dry the sheets on kitchen towels. After allowing the eggplant slices to “sweat” for at least 30 minutes, rinse them very well, one by one under running water, rubbing them, and then rinse again (more than you think you need). Now dry them (again… more than you think you need!) with paper towel. Heat the frying oil in a deep pan (I know it’s scary, but use a ton of oil. Like, close to 1 quart. The less oil you use, the more oil the eggplant will absorb – because the oil temperature will be more likely to drop when you drop the slices in). If you like using food thermometers, heat the oil to about 330-340F, or just do what I do: test it by dropping a tiny cube of bread or eggplant into it, and if lots and lots of tiny bubbles form around it, you are good to go. Fry the eggplant slices in batches (do not overcrowd the pan, or you’ll lower the temperature of the oil, ending up with greasy soggy slices). Oh, and I almost forgot: use tongs to put the slices in the oil, they are too heavy to be dropped in without getting splashed with hot oil. Fry on both sides until golden, and dry them on several layers of paper towel. Feel free to press the paper towel into the eggplant if you want to remove even more oil. Chop finely, setting only 4 or 5 whole slices aside. Brush a baking pan with little oil and start with a thin layer of the tomato sauce. I like to use earthenware but other materials also work, and as far as size you can go with something about 12 x 9 ½ in. Combine the rest of the sauce with the chopped fried eggplant. Alternate layers of lasagna, eggplant sauce, and ricotta, dusting each layer with little grated cheese. Decorate the top layer with the whole fried eggplant slices and extra grated cheese. Bake in a pre-heated oven at 350 F for about 30 minutes.