How to Make It
Preheat the oven to 350°. Prick the eggplant all over with a fork and set it on a baking sheet. Roast in the center of the oven for 1 hour, until very soft and collapsed. Let cool slightly, then scrape the eggplant flesh into a large bowl and let cool completely. Discard the skin.
Meanwhile, in a heatproof bowl, cover the porcini with 1 1/2 cups of boiling water and let stand until softened, 30 minutes; drain, reserving the soaking liquid. Rinse the porcini to remove any grit. Finely chop the porcini.
In an enameled cast-iron casserole, heat the olive oil until shimmering. Add the onion and half of the garlic and cook over moderately high heat, stirring, until softened, 5 minutes. Add the tomato puree and pour in the porcini soaking liquid, stopping before reaching the grit; bring to a boil. Simmer over moderately low heat, stirring, until thickened, 1 hour. Add half of the chopped basil and season with salt and pepper.
Fold the chopped porcini, bread crumbs, eggs, 2 ounces of cheese, parsley and the remaining garlic and chopped basil into the eggplant. Season with 1 teaspoon of salt and 1/2 teaspoon of pepper.
Line a baking sheet with wax paper. Form the eggplant mixture into twenty 1 3/4-inch balls, rolling tightly. Dust the balls with flour and refrigerate for 20 minutes.
In a large nonstick skillet, heat 1/2 inch of vegetable oil. Add half of the meatballs at a time and cook over moderately high heat, turning occasionally, until browned all over, about 8 minutes. Drain on paper towels. Add the meatballs to the tomato sauce and simmer for 5 minutes. Garnish the meatballs with basil leaves and serve with crusty bread and grated cheese.