1. Heat olive oil in a large pot over medium heat. Add the chopped onion and cook until translucent.
2. Add the sweet potatoes and apples to the pot. Cook for about 5 minutes, stirring occasionally.
3. Pour in the vegetable broth, then add the cinnamon and nutmeg. Bring to a boil, then reduce heat and simmer for 20 minutes, or until the sweet potatoes and apples are tender.
4. Use a blender to puree the soup until smooth. Season with salt and pepper to taste.