On a plate with a paper towel, place a layer of 2-3 slices of eggplant onto the towel. Sprinkle eggplant with sea salt. Repeat layers of eggplant sprinkled with sea salt until all eggplant slices are stacked, separated with towels. Place 2 paper towels on top of the stack and place a plate on top of the towels. Lay a heavy book or can of food onto the plate to squeeze out moisture. Allow to drip for at least 20 minutes, but up to 2 hours. Rinse and pat dry.
Beat eggs with milk in a shallow bowl. Place bread crumbs into separate bowl. Dip eggplant slices in the egg mixture and gently press into the crumbs to coat; set aside.
Preheat oven to 350*. Grease an 8X8-inch baking dish.
Heat olive oil in a large skillet over medium-high heat; fry eggplant slices in the hot oil in small batches until golden brown, about 1-2 minutes per side. Drain on paper towels.
Pour 1/2 cup marinara sauce into the bottom of the prepared baking dish and arrange a layer of eggplant slices to cover the sauce. Scatter basil and a few slices of smoked mozzarella cheese over eggplant; repeat layers, ending with a layer of sauce on top. Sprinkle Parmesan cheese over the top. Bake at 350* for 30 minutes.