Preheat the 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 black pepper on a rimmed baking sheet. Bake, stirring once or twice, until golden brown and tender, 12 to 15 minutes. Set aside.
Heat 2 tablespoons of the 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 tomatoes and 1 cup of water. Increase the heat to medium-high and bring to a simmer. Reduce the heat slightly, add the basil and simmer rapidly, uncovered, until thickened, 15 to 20 minutes. Discard the basil and season with salt and black pepper.
Meanwhile, heat the remaining 1 tablespoon oil in a medium skillet over medium heat. Add the pancetta and cook, stirring occasionally, until browned and crispy, about 8 minutes. Transfer to a large bowl with a slotted spoon.
Cook the fusilli in the salted boiling water until very al dente, about 2 minutes less than the package directions. Drain the pasta and add it to the bowl.
Add the tomato sauce, butternut squash, half of the mozzarella 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 mozzarella and Parmesan. Bake, uncovered, until browned, about 15 minutes. Let the pasta stand about 10 minutes before serving.
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