Skin the monkfish and cut it in half. Make incisions in the skin side of each sole fillet and fold them in two, with the incisions inside.
Despatch the crawfish in the way recommended. (If anyone offers to sell you a dead crustacean, don’t touch it. Whatever you pay will be too much as you won’t be able to do anything with it.) Take a stout pair of kitchen scissors and cut off the legs of the crawfish and put them on one side. It is important not to start dismembering the crawfish until the last moment, less than 10 minutes before you want to cook it.
Put 2 tablespoons olive oil and 2 tablespoons chopped onion into a 25 cm (10 inch) shallow saucepan and let them turn pale golden, stirring with a wooden spatula. Add the tomato purée and mix well. Add the crushed clove of garlic – flattened with the blade of a knife – then the thyme, bayleaf and fennel and the legs of the crawfish. Arrange the two crawfish halves, shell sides down, and the monkfish fillets on this bed, and spread out the sole fillets on top. Flame with the cognac or armagnac, and when the flames have died down add the vermouth and white wine. Do not add salt. Cover the pan and cook for 5 minutes over a medium heat, then add 3tablespoons or more of hot water. Continue to cook for 10 minutes more then remove the saucepan from the heat and set aside in a warm place, covered.
While the fish and crawfish are cooking, put the egg yolk into a large bowl with 2tablespoons of tepid water, whisk well, then gradually add 4tablespoons of olive oil in a thin stream, whisking constantly as though you are making a mayonnaise.
Melt the butter in a frying-pan and fry the slices of bread until they are a pretty pale golden colour. Set aside on a plate to keep hot.
Arrange the crawfish halves and legs and the fillets of monkfish and sole carefully on two hot soup plates. Cover with two more plates and keep hot. Strain the cooking liquid through a fine wire sieve into the bowl containing the egg/oil emulsion (4), whisking gently throughout and pressing down the debris to extract the juices. Wash out the saucepan and pour the contents of the bowl into it. Still whisking, replace it over a moderate heat. Take the pan off the heat before it boils or the egg will coagulate, whereas the object is to thicken the liquid lightly. Stir in the chopped parsley and season with salt and pepper. Divide the liquid between the two plates and serve as soon as possible, with the croûtons (5) handed separately.
white wines from the Côtes de Provence or white Graves