Grease the bottom and insides of the springform pan with softened butter. Mix 1/4 cup of the breadcrumbs with 2 tablespoons of the Parmigiano cheese. Coat the inside of the pan well with the cheese mixture. Knock out any excess and discard.
Heat 3 tablespoons of the oil in a large saute pan over medium heat. Add the ground beef and sprinkle with salt and black pepper and saute until cooked through. Add the garlic and cook until fragrant. Stir in the red wine and simmer until reduced by half, about 5 minutes. Add 4 cups of the red sauce and bring back to a simmer. Cook for another 5 minutes and season with salt and black pepper. Reserve the remaining red sauce for another use.
Meanwhile, peel the outer skin off the eggplant and using a mandolin slicer, slice the eggplants lengthwise into 1/4-inch-thick planks. Heat 3 tablespoons oil in a large skillet over medium-high heat. Sprinkle the eggplant with salt and black pepper and fry in a single layer, working in batches, until golden brown, about 3 minutes per side. Repeat with the remaining eggplant, using 3 tablespoons of oil per batch. You want to end up with enough eggplant planks to cover the bottom of the pan, the edges and the top of your Incaciata. Remove from the oil and drain on a paper-towel-lined baking sheet.
Combine the cooked pasta with the mozzarella and ragu sauce in a large bowl.