Cut the carrots, onions and parsley stalks into very small dice and cook to a light brown in the butter together with the thyme and bay-leaf. Wash the crayfish, remove the trails then cook the crayfish with the Mirepoix until they turn red.
Season with 12 g (⅓ oz) salt and a little milled pepper, sprinkle with the brandy and the wine and allow to cook gently to reduce. Add 2½ dl (9 fl oz or 1⅛ U.S. cups) White Bouillon and allow to cook gently for 10 minutes.
Cook the rice in 7½ dl (1⅓ pt or 3¼ U.S. cups) of the White Bouillon.
Shell the crayfish and reserve all the tails and ten of the heads.
Finely pound the remainder of the shells, add the rice and its cooking liquid together with the cooking liquid from the crayfish.
Pass through a fine sieve and dilute this purée with 5 dl (18 fl oz or 2¼ U.S. cups) White Bouillon. Bring to the boil, pass through a fine strainer and keep in the Bain-marie.
Finish the soup before serving with 150 g (5 oz) butter and 1 dl (3½ fl oz or ½ U.S. cup) cream; correct the seasoning and add a little Cayenne.