Heat the butter in a saucepan, add the onion and fry gently for 5 minutes until softened. Add the brandy and when boiling, flame with a long match and quickly stand back. As soon as the flames have subsided stir in the rice and add the stock.
Scoop the dark and white crab meat out of the shell into the pan and then mix in the chopped anchovies and paprika. Season with a little salt and cayene pepper then bring to the boil. Cover and simmer for 20 minutes.
Allow the soup to cool slightly then purée in batches in a blender or food processor. Pour back into the saucepan and stir in the milk and cream. Reheat, but take care to bring just to the boil and then reduce the heat to a simmer, stirring until hot all the way through. Taste and adjust the seasoning if needed.
Pour into teacups. Pick out the crab meat from the extra crab (if using) and flake into pieces. Serve in a separate bowl for diners to sprinkle over their soup and garnish with a little extra paprika.