• Preheat the oven to 400 degrees.

Eggplant Rollatini

• Trim the stems and ends from the eggplants. Remove strips of peel about 1 inch wide from the eggplants, leaving about half the peel intact. Slice the rounded sides from two opposite sides so that the eggplant sliced will lie flat. Slice the now flattened eggplant a scant ½ inch thick lengthwise (to get about 16 slices). Chop the ends you cut off, and set them aside.
• Heat about ½ inch vegetable oil in a large skillet over medium heat until the edge of an eggplant slice sizzles on contact. Spread some flour on a plate. Season the eggplant slices with salt, and dredge them in the flour. Fry, in batches without crowding, until they’re tender and golden, about 3 minutes per side. Drain on a paper-towel-lined baking sheet.
• For the filling: In a large bowl, combine the ricotta, shredded mozzarella, ½ cup grated Grana Padano, the parsley and the egg. Season with 1 tsp salt and stir to combine. Lay the eggplant slices out on your work surface with the top end toward you. Divide the filling among the slices, and roll them up.

Tomato Sauce and To Serve

• Carefully pour the oil out of the skillet and wipe it clean. Add the olive oil, and heat it over medium heat. Add the reserved chopped eggplant and cook until it’s lightly browned, 2 to 3 minutes. Scatter in the garlic and cook until it’s sizzling, about 1 minute. Add the tomatoes and season with 1 tsp salt. Cook, tossing occasionally, until the tomatoes begin to wilt on the edges, 2 to 3 minutes. Add ½ cup water, cover and simmer until the tomatoes have broken down and the mixture is saucy, 10 to 15 minutes. Stir in the basil.
• Nestle the rolls, seam side down, in the sauce, spooning a little of the sauce over each as you go. Sprinkle with the remaining 1 cup grated Grana Padano. Bake until the rollatini are browned and the sauce is bubbly, 25 to 30 minutes.