Preheat the oven to 500 degrees F. (Make sure your oven is clean!) Place three (6-inch) gratin dishes on a sheet pan and set aside.
Boil a large pot of water, add a tablespoon of salt, and add the pasta. If you're using one type of pasta, cook it for 1 to 2 minutes less than the directions on the package. If you're using two kinds of pasta, start with the one that cooks longest and add the second later so they finish at the same time. You want the pasta to be quite al dente. Drain.
Pour the Tomato and Eggplant Soup into a large bowl, add the cooked pasta, the mozzarella, 2 tablespoons of the Parmesan, 1 1/2 teaspoons salt, and 3/4 teaspoon pepper and toss well. Divide the mixture evenly among the three gratin dishes, dot the tops with the butter, and bake for 10 minutes, until hot and bubbly and the pasta begins to brown. Sprinkle each dish with 1 tablespoon of the remaining Parmesan, bake for another 4 minutes, and serve hot.
Tomato and Eggplant Soup:
Heat 1/2 cup olive oil in a medium (10 to 11-inch) pot or Dutch oven, such as Le Creuset, over medium heat. Add the eggplant and saute for 5 minutes, stirring frequently, until tender. Add a little more olive oil if the eggplant is sticking.
Add 2 tablespoons olive oil to the pot, add the onions and fennel, and cook for 6 to 8 minutes, stirring occasionally, until the onion is tender but not browned. Add the garlic and cook for one minute, stirring often. Add the chicken stock, crushed tomatoes, fennel seeds, oregano, thyme, red pepper flakes, 1 tablespoon salt, and 2 teaspoons black pepper. Pour the can of whole tomatoes, including the liquid, into a food processor and pulse until the tomatoes are coarsely chopped. Add the tomatoes and the liquid to the pot. Bring to a boil, lower the heat, and simmer uncovered for 15 minutes, stirring occasionally. Taste for seasonings. Serve hot in large bowls sprinkled with Parmesan cheese and a drizzle of olive oil.