Preheat oven to 450 degrees F. Bring a large pot of salted water to a boil.
Toss the squash with 2 tablespoons of the oil and 1/4 teaspoon each salt and pepper on a rimmed baking sheet. Bake, stirring once or twice, until golden brown and tender, 12 to 15 minutes.
Meanwhile, heat the remaining 2 tablespoons of oil in a medium saucepan over medium heat. Add the garlic and red pepper flakes and cook, stirring, until the garlic is golden, about 2 minutes. Add both cans of the tomatoes and 1 cup of water. Increase the heat to medium-high and bring to a simmer. Reduce the heat slightly, add the sage and simmer rapidly, uncovered, until thickened, 15 to 20 minutes. Stir in the ricotta and season with salt and pepper.
Cook the fusilli in the salted boiling water until very al dente, about 2 minutes less than the package directions. Drain the pasta and transfer it to a large bowl.
Add the tomato sauce, cooked squash, 1 cup of the mozzarella, the gorgonzola, and half of the Parmesan to the bowl and stir well to combine. Transfer the pasta to a 3- to 4-quart baking dish and top with the remaining 1 1/2 cups mozzarella and Parmesan. Bake, uncovered, until browned, about 15 minutes. Let the pasta rest for about 10 minutes before serving.
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