Hit the lemongrass with back of knife blade along stalk to bruise, then cut into 1-inch lengths.
In slow cooker, combine squash, coconut milk, chicken stock, curry paste, ginger, lemongrass, fish sauce, and brown sugar. Cover and cook on low for 4–6 hours or until squash is tender. Discard ginger and lemongrass.
Using a whisk, mash and stir squash to smooth the soup.
Stir in shrimp, cover and cook on high for 15 minutes, or until shrimp is firm and pink. Stir in the fresh mint or basil and serve.