Add the butter to a large Dutch oven over medium heat. When the butter is melted, add the breadcrumbs and toast until golden, 2 to 3 minutes. Transfer to a plate and set aside.
Heat the olive oil in the Dutch oven until hot. Add the garlic, eggplant and onion, season with the salt and cook, stirring, until softened, 1 to 2 minutes. Add the tomatoes, pasta, chicken stock, red pepper flakes and basil. Bring to simmer, cover and cook, stirring occasionally, until the pasta is al dente, 12 to 15 minutes.
Remove the lid and stir in the Parmesan and mozzarella. Turn off the heat and continue to stir until the cheese has melted and the sauce is thick.
Serve garnished with plenty of toasted breadcrumbs, Parmesan, parsley and basil.