Toss together the carrot, onion, apple, olive oil, ¼ teaspoon salt, and ⅛ teaspoon black pepper on the baking sheet and spread out in an even layer. Roast until everything is tender and starting to turn golden in spots, about 30 minutes, stirring once halfway through.
Heat 1 tablespoon butter in a medium-sized soup pot over medium heat; once melted, add the garlic, ginger, turmeric, cinnamon, nutmeg, and remaining ¼ teaspoon salt and remaining ⅛ teaspoon black pepper; cook 30 seconds, stirring constantly. Add the stock and roasted vegetables, and turn the heat off.
Puree the soup using an immersion blender (or puree it in batches in a regular blender). Transfer the soup back to the pot and bring to a simmer over medium heat. Taste and season with additional salt as desired.
While the soup is coming to a simmer, heat the remaining 1 tablespoon butter and the paprika in a small saucepan over medium-low heat. Once melted, cook until the butter starts to smell nutty and turn golden, about 1 minute, whisking constantly.
Ladle the soup into individual bowls and serve topped with paprika brown butter, creme fraiche, and chives.
This is an incredibly delicious soup. I slightly adapted this from a recipe I found on An Edible Mosaic.