Slice the eggplant in rounds just shy of ½-inch thick. Salt the eggplant and place the rounds in even layers divided by paper towels on a sheet pan. Rest for 30 minutes to 1 hour.

While the eggplant sweats, make the marinara sauce. Pour the tomatoes and purée into a bowl and crush with your hands or the back of a spoon, then set aside.

In a cold, large skillet, add the extra-virgin olive oil and garlic cloves, and bring to medium heat. As the garlic begins to sizzle, stir occasionally, and cook until fragrant and golden, about 5 minutes. Monitor the heat so the garlic doesn't cook too quickly or burn. Very carefully stir the tomato paste into the garlic and oil—take care so the oil doesn't splatter and burn you as the paste is added—and cook for 1-2 minutes. Carefully spoon the tomatoes into the pan with the oil and paste and season with salt and pepper. Add the basil sprigs and bring to a boil. Reduce to a bubbling simmer over low heat, stirring occasionally, for 30 minutes. Add water if the sauce becomes too thick. Stir to mix the oil that rises to the top, then discard the basil sprigs and garlic.

Next, prepare the eggplant. Pat the eggplant with a paper towel to remove excess moisture and salt. In separate shallow bowls, add the flour, beaten eggs, and breadcrumbs mixed with Parmesan cheese. Working one by one, dip an eggplant round in the flour (shake off the excess), then the egg, then the breadcrumb cheese mixture. Transfer the coated eggplant to a sheet pan fitted with a drying rack. Repeat the dredging with all of the eggplant and allow to sit for about 15 minutes so the breaded surface dries out.

Heat ¼-inch oil to 350°F in a large cast iron skillet or heavy-bottom skillet over medium-high. Working in batches of 5-6 slices, place the eggplant in a single layer in the skillet. Cook the eggplant for 3-4 minutes, then flip and repeat on the other side. Transfer to a paper towel-lined sheet pan and repeat with the remaining eggplant. Add more oil to the skillet as needed.

Spread 1 cup marinara sauce over the bottom of a 9×13-inch baking dish. Layer 12 slices of eggplant, overlapping the slices if needed. Spread 1 cup of the sauce over eggplant (I like to divide that amount between each row, going down the center of the rounds so the edges of the eggplant aren't sauced and stay crisped.) Sprinkle with half of the shredded mozzarella cheese and Parmesan cheese. Add another layer of fried eggplant, top with the rest of the sauce, and the rest of the cheese.

Cover the dish with foil and bake at 400°F for 30 minutes until the cheese is melted and the sauce is bubbling. Cool for 10 minutes before serving.