Preparation In a large saucepan over medium heat, cook bacon until rendered and crisp, 8 to 10 minutes. Transfer bacon to a paper towel–lined plate. Pour off all but 1 teaspoon of the fat. In the same saucepan, melt the butter, and add the carrot, celery, leek, and shallots. Season with salt and pepper. Cook over medium-low heat until softened and golden brown, 8 to 10 minutes. Add broth and chestnuts to the saucepan. Bring to a simmer, partially cover, and cook until all the ingredients are soft, about 30 minutes. Let cool slightly, and purée in batches in a blender until very smooth. Return to saucepan, add the cream, and heat thoroughly, adding stock to thin if needed. (A spoon should not leave a trail on the surface of the soup.) Season with salt and pepper and ladle into warmed shallow bowls. Garnish with the reserved bacon, a dab of crème fraîche, chives, and a pinch of nutmeg. DO AHEAD:The soup base can be made completely ahead of time and refrigerated for up to 2 days. Reheat, adding the cream just before serving.