Bring a large pot of salted water to a boil. Cook the pasta for about 8 minutes, or 2 minutes less than the package directions. Drain, reserving 1 cup of the pasta water.
Meanwhile, toss the eggplant with 1 tablespoon salt in a colander; allow to sit for 5 minutes. Rinse with cold water, then squeeze out the excess moisture. Dry well on a paper towel-lined tray.
Heat 2 tablespoons of the oil in a large straight-sided pan over medium heat. Add the sausage and cook, breaking it up with a wooden spoon, until cooked through and beginning to brown, about 6 minutes. Push the sausage off to one side, add the eggplant and cook without stirring for about 3 minutes. Stir together the eggplant and sausage and continue to cook, stirring often, until the eggplant is soft and beginning to brown, about 5 minutes. Stir in the shallots and garlic; cook for another 2 minutes. Deglaze the pan with the reserved pasta water, scraping up any browned bits. Stir in the tomatoes and the remaining 2 tablespoons olive oil and simmer for about 8 minutes, stirring often and breaking up the tomatoes.
Add the pasta to the sauce and sprinkle the Parmesan and provolone on the bare pasta. Using two wooden spoons, toss to combine until the cheese is melted and the sauce is creamy and coats the pasta.