Bring a large (4-6 quarts) pot of water to a boil and add 3 tablespoons salt.
Slice eggplant in half lengthwise, then slice each in half again. Slice crosswise into ½-inch thick pieces.
Whisk together egg, 1 teaspoon salt, pepper, garlic and oregano in a large bowl. Add eggplant and toss to coat. Dredge eggplant in the panko crumbs on a cookie sheet.
Place a large rimmed baking sheet on the oven rack and heat for 10 minutes.
Pour enough olive oil over the bottom of the preheated baking sheet to cover to a depth of 1/4-inch. Lay eggplant on the pan and roast 12 minutes. Flip eggplant slices over with a spatula, and roast an additional 10 minutes or until eggplant is tender and crust is golden.
Meanwhile, heat a medium saucepan over moderate heat. Add butter and heat until foaming subsides and butter is melted. Whisk in flour; cook 1 minute. Slowly pour in milk while whisking. Bring to a simmer, then lower heat and cook 5–10 minutes, whisking occasionally, until thickened. Remove from heat and stir in 1/4 cup of the Parmesan, 1/2 teaspoon salt and freshly ground black pepper.
Cook pasta according to package directions, until al dente. Drain.
Lower oven temperature to 400 (200 C) degrees. Combine the pasta with the milk sauce and transfer to a large casserole or baking dish. Top with the eggplant (and any crisp crumbs in the pan), marinara, remaining Parmesan and mozzarella cheese. Bake 12-15 minutes, until hot and cheese is melted. Sprinkle with parsley and serve.
Notes
This is a hearty dish that will easily feed a hungry table of 4, with leftovers.
Keep this in mind for a weekend dish, since it does involve multiple pots, pans and baking sheets.
Save time by using prepared marinara sauce and making the white cheese sauce up to 2 days ahead (keep refrigerated).
Bake the eggplant and boil the pasta just before assembling and baking.