Preparing the nage and the crayfish
Put the thinly-sliced carrot, leek, celery, shallots and onion in a saucepan with 1 teaspoon butter and 4 tablespoons water. Salt lightly, and cook over a very low heat, covered, for 20 minutes. (This slow cooking process is known as étuver.) Then add 400 ml (scant ¾ pint) white wine and the little bag of herbs and spices, and simmer for 15–20 minutes. Watch the seasoning and the cooking time very carefully, as the vegetables should keep a trace of ‘bite’ to their texture. Remove the little parcel of herbs.
While the vegetables are cooking, bring 4 litres (7 pints) of water, seasoned with 2 tablespoons of coarse salt, to the boil and plunge in the crayfish. When the water has come back to the boil, cook for 4 minutes. Then lift out the crayfish with a slotted spoon and drain them in a colander. When they have cooled slightly, detach the tails and shell them by pinching the carapace between your thumb and forefinger. Keep the flesh, together with two of the head-shells, on one side.
Preparing the beurre blanc
Take a small saucepan with sloping sides and put into it two coarsely-chopped shallots, the remaining white wine and 3 tablespoons wine vinegar. Reduce over a brisk heat watching attentively until only 2 tablespoons of liquid are left. If you find you have overdone the reduction, stretch it with a little of the nage (1). Remove the pan from the heat and, little by little, incorporate 110 g (scant 4 oz) butter, cut into large dice, whisking vigorously, until you have a sauce the consistency of cream. Season with salt and pepper. If the sauce curdles, because you have overdone the heat or added the butter too quickly, you can put two tablespoons of the nage (1) into another saucepan and pour the curdled sauce in to it in a trickle, whisking all the time. You can keep the sauce hot by putting a folded newspaper in the bottom of a large saucepan, placing the pan containing the beurre blanc on top of the paper, and putting the whole thing on the edge of the hot-plate where it will keep warm without overheating.
Finishing the dish
Bring the nage (1) to the boil and add the crayfish tails (2), the beurre blanc (3) and the parsley and chervil sprigs and tarragon leaves. Bring back to the boil for an instant, taste and add more salt and pepper if necessary.
Divide the soup between two bowls or plates and place a crayfish head standing upright in the middle of each.