Heat 1/2 cup of oil and the butter in a large saute pan over medium heat. Add the onion and eggplant and cook gently over medium heat for 10 to 15 minutes, stirring often, until tender. It may be necessary to add more oil as the eggplant soaks the oil up quickly. Towards the end of cooking time, add the whole garlic cloves and half of the basil leaves.
In the meantime, bring a large pot of salted water to a boil and blanch the tomatoes for 4 to 5 minutes until the skin splits and the tomatoes are softened. Remove the tomatoes with a slotted spoon and place them in a mesh colander set over a large bowl. Reserve the cooking liquid.
When they are cool enough to handle, core the tomatoes and peel off the skin. Using clean hands, squish the tomatoes, pushing the pulp through the sieve into the bowl underneath. At first you will have a watery liquid. Add the tomato liquid to the eggplant and then continue to push the tomato pulp through the sieve, until you have only seeds and hard pulp pieces left. Finally, add the rest of the pulpy liquid to the eggplants and season with salt and pepper to taste. Add the sugar and continue to cook for 10 more minutes, until thickened.
In the meantime, bring the reserved cooking liquid back to a boil, add additional salt, and cook the fettuccine according to directions on the package. Drain well.
To serve, spoon a third of the eggplant into a bowl and set aside. Toss the pasta in the saute pan with the remaining eggplant and add the packaged mozzarella. Place the mixture in a large serving bowl and top with the reserved eggplant, the fresh mozzarella and the Parmesan. Garnish with the remaining basil leaves and serve hot.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.