How to Make It
Preheat the oven to 375°F.
In a large pot of boiling salted water, cook the pasta until al dente, then drain.
In a medium heavy pot with a lid, simmer the squash with the shallot, chicken broth, oil, 3/4 teaspoon salt and 1/2 teaspoon pepper until the squash is very tender, about 25 minutes. In a food processor, pulse the squash mixture until smooth. Season with salt and pepper to taste. Toss the pasta with the squash puree and transfer to a 3-quart baking dish. Spread the cheese over the top of the pasta and bake until the cheese is melted and the filling is bubbling, 25 to 30 minutes.