Add the frozen squash and vegetable broth to the skillet. Cover and simmer for 10 minutes until the squash is tender.
Transfer the squash mixture to a blender. Add the vegan grated cheese, coconut milk, salt, and black pepper. Blend until completely smooth.
Pour the blended mixture back into the skillet. Toss with the cooked pasta, splashing in the reserved pasta water as needed to reach the desired consistency. Serve warm.