Make the soup: Melt the butter in a soup pot over low heat. Cook the onion in the butter, stirring occasionally, until very soft but not browned, 10 to 13 min. Add the garlic, ginger, and cardamom and cook for another minute. Increase the heat to high and add the jalapeño, sweet potatoes, 4 cups of the broth, and the salt. Bring to a boil, reduce the heat to medium low, cover, and simmer until the potatoes are very soft, 15 to 20 min.
In a blender, purée the soup in batches until very smooth. Rinse and dry the pot and return the puréed soup to it. Add the remaining broth and the cream, if using, and bring to a simmer over medium-low heat. Add the lime juice and brown sugar, and season with salt and white pepper to taste.
Make the raita: While the soup is simmering, combine the yogurt, apple, mint, and jalapeño in a small bowl. Season with salt and pepper to taste. Refrigerate until ready to serve.
To serve: Ladle the soup into individual bowls and add a dollop of the raita.