How to Make It
In a large nonstick frying pan, heat 1 tablespoon of the oil over moderate heat. Add the onion and garlic and cook, stirring occasionally, until the onion starts to brown, about 5 minutes. Remove. Heat 6 tablespoons of the oil in the same pan over moderately high heat. Add the eggplant and cook, stirring occasionally, until golden, about 10 minutes. Add the onion mixture, fresh and canned tomatoes, parsley, and 1 teaspoon of the salt. Simmer until thick, about 10 minutes. Stir in the pepper.
Meanwhile, in a medium saucepan, bring the water and the remaining 1 1/4 teaspoons of salt to a boil. Add the cornmeal in a slow stream, whisking constantly. Whisk in the remaining 3 tablespoons of oil. Reduce the heat and simmer, stirring frequently with a wooden spoon, until the polenta is thick, about 20 minutes. Stir in the Parmesan. Serve the hot polenta topped with the vegetables.