Slice the eggplant into 1/2-inch thick rounds. Lay the slices in a single layer across two large baking sheets lined with paper towels. Lightly salt both sides of each eggplant slice and allow them to sit for 45 minutes. Once time has passed, pat each slice dry with paper towels to remove any excess moisture.
Set out three separate bowls or plates for the dredging process. In the first, place the flour. In a shallow bowl, whisk the eggs and milk until combined. In another shallow bowl, mix together the panko breadcrumbs, parmesan, salt, and black pepper.
Start by dredging 2 to 3 slices of eggplant at a time. First, coat the slices in flour, ensuring an even layer. Then, dip each slice into the egg mixture, allowing any excess to drip off. Finally, press the eggplant into the breadcrumb mixture, coating it fully on both sides.
Preheat your oven to 200°F to keep the fried eggplant warm.
In a large skillet, heat vegetable oil over medium-high heat until it reaches about 350°F. You’ll need enough oil to cover the skillet about 1/4-inch deep. Fry 4 to 5 eggplant slices at a time in a single layer, cooking for approximately 3 minutes or until golden brown on both sides. Transfer the fried eggplant to a wire rack placed over a sheet tray or use paper towels to absorb excess oil. Keep the fried eggplant warm in the oven while you cook the remaining slices, adding more oil to the skillet as necessary.
Before serving, garnish the fried eggplant with freshly chopped parsley and a pinch of salt. Marinara sauce on the side is a great addition for dipping.