Cook the pasta according to the box’s directions. Make sure to reserve 1 cup pasta water before draining.
Warm the oil in a large skillet over medium heat. Add the squash, onion, garlic, sage, and red pepper flakes to the skillet. Cook, stirring occasionally, until the onion is translucent, about 8 to 10 minutes. Add the broth, and season with salt and pepper. Bring the mixture to a boil, then reduce the heat and simmer until the squash is soft and the liquid is reduced by half, about 15 to 20 minutes.
Once the squash mixture is done cooking, transfer it to a blender, and purée until smooth (beware of hot steam escaping from the top of the blender).
Back in the skillet, combine the pasta, squash purée and ¼ cup pasta water. Toss together, adding more water as needed, until the sauce coats the pasta.