Salt the eggplant: In a large bowl, on a baking sheet, or directly on a cutting board, sprinkle 1 teaspoon of salt evenly all over the eggplant slices. Lay out a few layers of paper towels on a large cutting board or baking sheet. Arrange about one-third of the eggplant slices in a single layer and cover with more paper towels. Continue stacking the eggplant and paper towels, finishing with a final layer of paper towels. Let sit for 1½ to 2 hours. Press on the paper towels to absorb any excess liquid before proceeding.
Combine the flour and ¾ teaspoon salt on a large plate. Whisk the eggs with 2 tablespoons cold water in a wide bowl. Mix the breadcrumbs with ¾ teaspoon salt on a large plate.
Lightly coat each slice of eggplant in the flour, shaking off excess. Dip in egg mixture, letting any excess drip off, then dredge in the breadcrumbs, pressing with your fingertips so the crumbs adhere. (Use one hand for the dry ingredients – the flour and breadcrumbs – and one for the egg mixture - it's much neater this way!) Set the breaded eggplant slices on a baking sheet.
Line another baking sheet with a few layers of paper towels. Pour enough oil into a large (12-inch) skillet to measure about ¼-inch deep and heat over medium heat until hot (if you dip a piece of eggplant into the oil, it will sizzle immediately). Working in batches, add as much eggplant as will fit in a single layer and fry, flipping once, until golden brown, about 3 minutes per side. Transfer to the paper towel-lined baking sheet. Repeat, frying the remaining eggplant and layering it between sheets of paper towels to drain.
Preheat the oven to 425°F and set an oven rack in the middle position.
Note: Nutritional information was calculated assuming that approximately ½ teaspoon of the salt sprinkled onto the eggplant was absorbed and ¼ cup of the oil is absorbed into the eggplant when frying.
Make-Ahead/Freezer-Friendly Instructions: The eggplant parmesan can be assembled up to 2 days before baking; it can also be frozen, baked or unbaked, for up to 3 months. (If freezing, defrost in the refrigerator overnight prior to reheating/baking.)