In a large stock pot, melt butter and add celery, carrots and onions. Cook to soften, about 7-8 minutes. There should be no color on vegetables.
Add parsley, cloves, bay leaf and chicken stock and chestnuts. Bring ingredients to a boil and reduce to a simmer and cook for 20 minutes.
Add Madeira. Cover the soup with a lid and cook for 5 minutes at a simmer.
Remove lid. If using an immersion blender, blend in same cooking pot. If using a blender, puree in batches until mixture is completely smooth with no visible chunks.
Strain pureed soup into a clean stock pot. Return to the heat and add heavy cream. Add black pepper to taste. Ensure the soup is extremely smooth. Use immersion blender again if needed. Serve warm.
This soup is perfect served with a quenelle of crème fraiche or dollop of sour cream. A light sprinkling of fresh chives adds the perfect finishing touch. Even more inviting, add a grilled piece of country bread rubbed with olive oil and garlic....perfect for sopping up that last bit in the bottom of your bowl!