Halve the squash and remove seeds. Place squash cut sides down in the pan and bake for 40 minutes, or until the squash is tender when pierced. Cool for 15 minutes.
Puree squash in blender or food processor, or place in a large pan and mash with fork or potato masher to remove large lumps. Add 1 1/2 cups water, vegetable juice, bell pepper, corn, basil, and salt. Bring to boil.
Reduce heat and simmer 10 minutes. Serve soup hot or cold.