Line a plate with a paper towel; place a layer of 2 or 3 slices of eggplant onto the towel. Sprinkle eggplant with sea salt. Repeat layers of eggplant sprinkled with salt until all eggplant slices are stacked. Place 2 paper towels onto 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 20 minutes to 2 hours. Rinse and pat dry.
Beat eggs with milk in a shallow bowl. Place bread crumbs into a separate bowl. Dip eggplant slices in the egg mixture and gently press into the crumbs to coat; set aside.
Preheat oven to 350 degrees F (175 degrees C). 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 to 2 minutes per side. Drain on paper towels.
Pour about 1/4 cup of 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 in the preheated oven until heated through and the cheese has melted, about 15 minutes. Serve immediately.