How to Make It
Light a grill or heat a grill pan and lightly oil the grate. Brush the eggplant slices generously with olive oil, season with salt and pepper and grill over moderate heat, turning occasionally, until lightly charred and softened, about 10 minutes. Transfer to a platter.
In a medium bowl, combine the ricotta with 1 cup of the mozzarella, 1/2 cup of the Parmesan, the eggs, parsley, 3 tablespoons of basil and 1/2 teaspoon each of salt and pepper. Fold the ricotta mixture with a rubber spatula until just combined.
Preheat the oven to 400°. Lightly brush a 9-by-13-inch baking dish with olive oil. Spoon 1 cup of the marinara sauce over the bottom of the dish. On a work surface, place 1 slice of grilled eggplant with a short side facing you. Spread 2 1/2 tablespoons of the ricotta filling over the eggplant. Roll up the slice and place it seam side down in the baking dish. Repeat with the remaining eggplant and filling. Spoon the remaining 1 cup of marinara over the eggplant rolls and sprinkle with the remaining 3/4 cup of mozzarella.
Cover the dish with foil and bake for about 30 minutes, until the sauce is bubbling and the cheese is beginning to melt. Remove the foil and bake for 12 to 15 minutes longer, until the cheese is lightly browned. Transfer the baking dish to a wire rack and let cool for 15 minutes. Garnish with the remaining Parmesan, sprinkle with minced basil and serve.