Heat olive oil in a large soup pot. Add carrot, celery and onion, and stir in the curry paste and the chopped ginger. Cook until vegetables are tender and ginger is aromatic, 3 to 4 minutes.
Add butternut squash, stirring to combine. Bring to a boil (add a little chicken broth if necessary), then reduce heat and simmer until squash is fork-tender, about 30 minutes. Stir in chicken broth and light or regular coconut milk. Season with salt and pepper; taste and adjust seasonings, if necessary.
Use an immersion blender to puree soup. Alternatively, let the soup cool slightly and carefully puree in batches in a traditional blender.
Garnish each serving with 1 or 2 pappadums, a tablespoon toasted coconut flakes and a tablespoon chopped fresh cilantro. A squeeze of fresh lime juice is also good. Enjoy!