1. Arrange the eggplant slices on a baking sheet or large cutting board and sprinkle evenly with 1 teaspoon of salt. Layer the slices between paper towels and let them rest for 1½ to 2 hours to draw out excess moisture. Pat dry before using.

2. To prepare the béchamel sauce, melt the butter in a small saucepan over medium heat. Whisk in the flour and cook for 2 minutes. Slowly add the milk while whisking until smooth. Bring to a gentle boil, then reduce heat and simmer for about 2 minutes until thickened. Stir in the Parmesan cheese, salt, and black pepper. Set aside.

3. In one shallow dish, combine the flour with ¾ teaspoon salt. In a second dish, whisk together the eggs and cold water. In a third dish, combine the breadcrumbs with the remaining ¾ teaspoon salt.

4. Coat each eggplant slice lightly in flour, then dip into the egg mixture, and finally press into the breadcrumbs until evenly coated. Place the breaded slices on a baking sheet.

5. Line a clean baking sheet or large plate with paper towels. Heat about ¼ inch of vegetable oil in a large skillet over medium heat. Fry the eggplant in batches for about 3 minutes per side, until golden brown and crispy. Transfer to the paper towels to drain.

6. Preheat the oven to 425°F.

7. Spread about ¾ cup marinara sauce in the bottom of a 9×13-inch baking dish. Arrange one-third of the eggplant slices over the sauce. Top with another ¾ cup marinara, 1 cup mozzarella cheese, and spoonfuls of béchamel sauce. Repeat the layers two more times, leaving some edges exposed on the top layer for extra crispiness.

8. Sprinkle the top with Parmesan cheese and bake for 30 to 35 minutes, until bubbly and golden brown.

9. Let the dish rest for about 20 minutes before serving. Garnish with fresh basil if desired.