Slice the eggplant lengthwise into twelve 1/8- to 1/4-inch-thick slices. Arrange the eggplant slices on a baking sheet and sprinkle both sides generously with salt. Set aside to draw out the moisture, about 40 minutes. Transfer the eggplant to a colander and rinse. Pat very dry with paper towels.
Meanwhile, make the tomato sauce: Heat 3 tablespoons olive oil in a large pot over medium-high heat. Add the onion and cook, stirring occasionally, until softened, about 5 minutes. Stir in the tomatoes, 1/2 cup water, the garlic, basil, sugar and 1 teaspoon salt. Bring to a boil, then reduce the heat and simmer until slightly thickened, 30 minutes. Discard the basil sprigs and puree the sauce with an immersion blender (or puree in a regular blender in batches).
Mix the flour and 1 teaspoon salt in a shallow bowl. Beat the eggs in a separate shallow bowl. Combine the breadcrumbs, 3 tablespoons Parmesan, the garlic powder, Italian seasoning, 1 teaspoon salt and 1/2 teaspoon pepper in a third shallow bowl. One at a time, dip each eggplant slice in the flour, then the eggs, then the breadcrumbs and transfer to a baking sheet.
Heat the remaining 3 tablespoons olive oil in a large nonstick skillet over medium-high heat. Add 4 eggplant slices and cook until golden brown and crisp, 1 to 2 minutes per side. Remove to a paper towel–lined baking sheet. Repeat with the remaining eggplant, adding more oil to the skillet as needed.
Meanwhile, bring a large pot of salted water to a boil. Add the lasagna noodles and cook as the label directs for al dente. Remove 1/2 cup cooking water, then drain the noodles. Stir the reserved cooking water into the tomato sauce.
Assemble the lasagna rolls: Preheat the oven to 375 ̊ F. Pour 5 cups of the tomato sauce into a 9-by-13-inch baking dish. Spread 1 tablespoon ricotta on a lasagna noodle; top with 1 tablespoon Parmesan, 3 heaping tablespoons mozzarella, another lasagna noodle and 2 eggplant slices to cover the length of the entire noodle. Top the eggplant with 2 heaping tablespoons of the tomato sauce. Starting with a short end, roll up the stack into a spiral. Use a sharp knife to slice the spiral in half to make 2 spirals. Place each piece in the baking dish cut-side down with the wavy edges of the noodle facing up. Continue with the remaining lasagna noodles and eggplant slices until you have 12 spirals in the baking dish. Top with any remaining ricotta, Parmesan and mozzarella.
Cover the dish with foil and bake until the cheese is melted and the sauce is bubbling, 20 to 25 minutes. Uncover and continue to bake until browned on top, 10 to 12 more minutes. Top with basil and serve with any remaining tomato sauce.
You can assemble these lasagnas in advance and freeze for up to 3 months. Let thaw in the refrigerator, then bake as directed.