Melt 40g of the butter with 1 tbsp of the oil in a saucepan. When foaming, add the prawn heads and shells and cook over a medium-high heat for 3-5 minutes, stirring regularly, until the mixture smells fragrant and the shells are orange. Add the fish stock and bring to the boil, then reduce the heat and simmer gently for 30 minutes.
Meanwhile, in a large saucepan, melt 30g of the remaining butter and 2 tbsp of the remaining oil over a low heat, then add the shallots, carrot, celery and garlic. Cook gently for 8-10 minutes until the veg are very soft but not coloured.
Increase the heat to medium, then add the bay leaf, parsley sprigs and tomato purée. Cook for 1 minute, stirring. Turn up the heat to high, then add the brandy or cognac and bubble until evaporated. Add the rice, prawn broth (including the heads and shells), cayenne pepper and tomatoes, then cook for about 20 minutes or until the rice is tender. Allow to cool slightly.
Remove the bay leaf from the pan, then ladle the soup into a blender, in batches, and whizz for 2-3 minutes until very smooth – hold a tea towel over the lid (without the stopper in) to let steam escape. Strain the soup, in batches, through a fine sieve into a medium bowl, pushing it through with a ladle (discard the solids left in the sieve).
Clean the sieve, then line it with muslin. Pass the soup through the muslin into a saucepan, add the lemon juice, cream and a dash more brandy or cognac, then taste and season (it probably won’t need much salt). Heat to a gentle simmer.
When the soup is hot and ready to serve, finely chop a little extra parsley. Heat the remaining 30g butter and 1 tbsp oil in a frying pan. When foaming, add the chopped prawns and parsley, then cook, stirring occasionally, over a high heat for 1-2 minutes until the prawns are pink. Ladle the soup into bowls, then top with the parsley and prawns.
