Heat olive oil in a large pot over medium heat. Add onion and cook until softened, about 5 minutes.
Add garlic and ginger and cook for 1 minute more.
Stir in red curry paste and cook for 30 seconds.
Pour in vegetable broth, sweet potatoes, and carrots. Bring to a boil, then reduce heat and simmer for 20-25 minutes, or until sweet potatoes and carrots are tender.
Carefully transfer soup to a blender (or use an immersion blender) and blend until smooth.
Return soup to pot and stir in coconut milk and lime juice. Season with salt and pepper to taste.