Preheat the oven to 375°F.
Peel the carrots and parsnips and cut into 2-inch pieces. Place in a 13 by 9-inch baking pan. Drizzle with olive oil and bake until the carrots and parsnips are golden and can be easily skewered, 45 to 60 minutes. Cool for about 20 minutes.
Melt the butter in a soup pot over medium heat. Add the onions and cook, stirring occasionally, until the onions are soft, about 10 minutes. Add the carrots and parsnips and stock and simmer 30 minutes. Let cool for about 20 minutes. In batches, puree the soup in a blender on high speed, 3 minutes per batch, until very smooth. Season to taste with salt and pepper. If the soup is too thick, correct the consistency with additional water or stock.
Place the crème fraiche and spices in a bowl and whisk together. Season with salt and pepper. Using water, a tablespoon at a time, thin the crème fraiche until it is the consistency of very heavy cream.
Ladle the hot soup into soup bowls. Drizzle a spoonful of the spiced crème fraiche onto the top. Garnish with parsley leaves and serve.