In a large heavy pot, heat oil over medium-high; add squash and onion. Cook until onion is soft, about 6 minutes.
Add corn and curry powder; cook until curry is fragrant, about 2 minutes. Season with salt and pepper.
Add broth and simmer until squash is tender, about 25 minutes. In a blender, blend half the soup until smooth. Return to pot and stir in cream; heat through over medium-low (do not boil).