Step 1

Heat the oven to 400°F with a rack in the middle position. Using a vegetable peeler and working from top to bottom, on each eggplant, peel off strips of skin spaced about 1 inch apart. Cut the eggplants crosswise into slices ½ inch thick, then arrange in a single layer on a baking sheet. Brush the eggplants on both sides with 3 tablespoons of the oil and season lightly with salt and black pepper. Roast until soft with some browned spots, 25 to 30 minutes, flipping the slices about halfway through.

Step 2

Meanwhile, in a large pot, bring 4 quarts water to a boil. Add the pasta and 1 tablespoon salt, then cook, stirring occasionally, until al dente. Reserve 2 cups of the cooking water, then drain. Set the pasta and cooking water aside.

Step 3

In the same pot over medium, heat 2 tablespoons of the remaining oil until shimmering. Add the sausage and cook, breaking it into small pieces, until starting to brown, 5 to 6 minutes. Stir in the tomatoes with juices, garlic, pepper flakes and ½ teaspoon black pepper. Bring to a simmer over medium-high, then reduce to medium-low and cook, uncovered and stirring occasionally, until the sauce is slightly reduced, 10 to 15 minutes. Stir in the basil and 1½ cups of the reserved cooking water. Remove from the heat and transfer 2 cups of the sauce to a small bowl. Stir the pasta into the sauce remaining in the pot, then taste and season with salt and black pepper.

Step 4

Brush a 9-by-13-inch baking dish with the remaining 1 tablespoon of the oil. Distribute half of the sauced pasta in an even layer in the prepared baking dish. Layer on the eggplant, overlapping the slices to fit, if needed. Spread half of the reserved sauce over the eggplant layer, covering it completely, then sprinkle with half each of the fontina and Parmesan. Distribute the remaining pasta evenly on top, followed by the remaining reserved sauce, then sprinkle evenly with the remaining fontina and Parmesan. Bake until the cheese is melted and browned in a few spots, 15 to 20 minutes. Cool for about 10 minutes before serving.