Preheat oven to 450°F. Place eggplants cut side down on a lightly oiled foil-lined broiler pan or baking sheet. Roast eggplant until it is very tender and lightly browned on top and bottom, about 45 minutes. Cool.

Meanwhile, heat olive oil in a large Dutch oven over medium heat. Add onion and sauté 5 minutes. Add garlic and cook for another minute. Scoop eggplant flesh from the skins; discard the skins. Chop flesh roughly and add to the pan along with tomatoes, water and salt and bring to a boil over high heat. Reduce heat to low, cover and simmer 20 minutes, stirring occasionally. Top each serving with 2 tablespoons of Parmigiano Reggiano, croutons and basil, if desired.