Heat the oil in a large soup pot over medium heat. Add the onion, garlic, and ginger and cook, stirring frequently, until softened, 6 to 8 minutes. Do not brown; reduce heat if necessary.
Add the squash, carrots, broth, and curry paste. Bring to a boil, then lower the heat and simmer, covered, until the vegetables are tender, about 20 minutes.
Using a hand-held immersion blender (or blender) , purée the soup until silky smooth. (Alternatively, cool the soup slightly, then purée in a blender in batches, making sure to leave the hole in the lid open to allow the steam to escape.) Stir in the coconut milk, lime juice, and salt (if the coconut milk is solidified, use the immersion blender to mix it in).
Bring to a simmer, then taste and adjust the seasonings, if necessary. Ladle the soup into bowls.