Heat a medium saucepan over medium-high heat. Add oil, swirl to coat. Add onion, cook 3 minutes. Add curry paste, garlic, and ginger; saute 45 seconds, stirring constantly.
Add the broth and the next 5 ingredients (through salt) and cover. Bring to a boil. Reduce heat, and simmer 10 minutes, stirring frequently. Place half the mixture into a blender. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clan towel over the opening in the blender lid. Blend until smooth. Pour into a large bowl. Repeat procedure with the remaining squash mixture.
Spoon 1 cup soup into each of 4 bowls; top with 2 tablespoons peanuts and 1 tablespoon cilantro. Serve with lime wedges.