Cook the penne according to package instructions. Before draining, reserve 2 cups of the starchy pasta water. Set aside.
In a large deep sauté pan, heat the olive oil and butter over medium heat. Add the cubed eggplant and cook until golden brown and softened. Remove the eggplant and set aside.
In the same pan, add the chopped onion and garlic. Sauté gently until the onions are translucent and fragrant. Stir in the anchovy fillets and cook until they melt into the onions, about 2 minutes.
Simmer the Tomatoes. Add both the chopped tomatoes and tomato sauce (do not drain). Stir to combine, cover, and simmer for 20 minutes, stirring occasionally.
Return the eggplant to the pan. Add 1 cup of the reserved pasta water. Stir in the olives, capers, red pepper flakes, parsley, basil, and thyme. Simmer uncovered for an additional 10 minutes. Season with salt and pepper to taste.
Add the drained pasta to the sauce, tossing gently to coat. Use reserved pasta water as needed to loosen the sauce and help it cling to the pasta.
Sprinkle with grated Parmesan cheese and serve hot.