Pia uses fresh tomatoes to make her parmigiana; when those aren’t in season, San Marzano whole Roma tomatoes are great for the sauce. Pia cooked her eggplant on Nancy’s big, round griddle; I like to brush my slices of eggplant with olive oil, and put them on a big sheet pan under the broiler to get them deep golden brown (see it here). I also am adding a little garlic to the sauce; Pia did not. Pia says to look for very firm, solid eggplant; those have fewer seeds.
In a 4-quart heavy saucepan, heat 2 tablespoons of olive oil over medium heat. Add the garlic and cook just until fragrant but not browned, about 30 seconds. Add the tomatoes and a handful of the torn basil leaves. Season with about 1 tablespoon of salt. Bring to a boil, then reduce the heat, cover, and simmer until the tomatoes are broken down and a the mixture is saucy, about 45 minutes, stirring occasionally. Taste and add more salt if needed.
Meanwhile, brown the eggplant. Line a heavy duty sheet pan with foil (nonstick foil works well) or parchment paper. Move a rack in the oven to the second shelf below the broiler. Brush both sides of the eggplant slices lightly with olive oil, and lightly salt them. Place the eggplant on the sheet pan and place under the broiler until deep golden brown, then flip the eggplant and brown the other side. Repeat with remaining eggplant.
Heat the oven to 375˚F and place a rack in the center of the oven.
Spoon a bit of the sauce in the bottom of a large casserole dish (or 13x9x2-inch baking pan). Place the eggplant over the sauce in a single layer in the bottom of the dish. Sprinkle the eggplant generously with mozzarella, parmesan, torn basil leaves, and sauce. Repeat, using all of the eggplant in three layers. Top with the whole basil leaves and finish with sauce and cheese. There may be some sauce, cheese, and eggplant leftover but it's better to have more than enough.
Bake the eggplant for about 45 minutes, or until the cheese is melted and golden brown.