In a large Dutch oven over medium heat, melt the butter until foamy. Add the carrots, celery, and onion, and cook, stirring occasionally, until softened, 5 to 8 minutes.
Add the chestnuts, thyme, stock, and duck confit or pork rillette, and bring to a boil. Reduce the heat to low and simmer until the vegetables are fully cooked, about 20 minutes. Add the heavy cream and simmer 5 minutes longer. Season with salt and pepper to taste.
In the blender, working in batches, carefully purée the soup until very smooth. As you are blending, season with salt and pepper to taste.
For the maple cream, whip the cream until very firm. Stir in just enough maple syrup to give it a sweet flavour.
Divide the soup among 4 bowls and garnish each with a tablespoon of duck confit, a spoonful of cream, and parsley.