Preheat the oven to 375° F. Line a baking sheet with foil or parchment paper.
Place about two-thirds of the squash on the baking sheet. Drizzle with olive oil and season with salt and pepper. Roast for 20 minutes, or until just tender. It will finish cooking with the mac and cheese.
Add the remaining squash to a microwave-safe bowl with 1/3 cup of water. Cover with plastic wrap and microwave on HIGH for 8 minutes, or until very soft. Drain and mash with a fork. Set aside.
In a large pot of salted water, cook the cavatappi pasta according to package directions or until just al dente.
Meanwhile, in a large sauté pan, melt 2 tablespoons of butter over medium heat. Add the onion and cook until softened, about 5 minutes. Stir in the garlic and sage. Cook for an additional minute, until fragrant. Season with salt and pepper.
Add the remaining 4 tablespoons of butter to the pan and let it melt. Add in the flour and dry mustard, stirring constantly for 1 minute, or until the mixture forms a thick paste.
Gradually whisk in the half-and-half and milk. Whisk constantly to avoid lumps. Cook until the sauce has come to a gentle bubble and thickens enough to coat the back of your spoon, about 4 minutes.
Remove the pan from the heat. Stir in 1 cup of the sharp cheddar, 1 cup of the mild cheddar, and 1/2 cup of the Parmesan until melted and smooth.
Add the roasted and mashed squash to the sauce. Stir until everything is fully combined. Taste and add salt and pepper as needed.
Add the drained pasta. Mix everything together until the pasta is well-coated and the squash is evenly distributed.
Lightly coat a 9x13-inch pan with cooking spray, then pour the mac and cheese mixture into the dish. Spread it into an even layer.
To make the breadcrumb topping, melt butter in a small sauté pan over medium-high heat. Add Italian seasoned breadcrumbs and stir frequently for about 3 minutes or until toasted and fragrant.
Sprinkle the toasted breadcrumbs evenly over the macaroni and cheese. Top with the remaining sharp cheddar, mild cheddar, and Parmesan. Bake for 30 to 40 minutes, or until golden brown and bubbling. Garnish with sage leaves.