Cut the carrots, onion and shallot into tiny mirepoix dice or, more simply, give them 15 seconds in the liquidiser.
Heat the olive and arachide oils in the sauté pan, throw in the crayfish and cook covered for 6 minutes to let them colour. Then, away from the heat, remove the crayfish with a slotted spoon, detach and shell the tails and put them on one side.