Preheat the oven to 425°F (220°C), with the oven rack positioned in the center.

Toss the butternut squash cubes on a rimmed baking sheet with the onion, olive oil, 1 teaspoon salt, crushed red pepper, and black pepper. Arrange in one layer. Roast for 15 minutes.

Add the garlic and sage to the roasting pan and stir the squash around. Continue roasting for 10-15 more minutes, or until the squash is tender and the onion is browned on the edges.

Scoop out 1 ½ cups of the roasted squash mixture from the sheet pan and set aside in a small bowl. Scrape the remaining squash, sage leaves, and pan liquid into a food processor.

Add 2 cups of the broth, ¼ cup of the Parmesan, and the butter to the processor. Puree until the sauce is completely smooth, adjusting the consistency with additional broth as needed. Keep the sauce warm while the pasta cooks.

Bring 4-5 quarts of water to a boil in a large pot, then add 2 tablespoons kosher salt. Cook the pasta until al dente and drain. Transfer to a large serving bowl.

Add the sauce to the pasta, along with the reserved roasted squash. Serve hot, with additional Parmesan cheese.