Melt half the butter in a saucepan, add the flour, stir, and allow to bubble for 2 or 3 minutes, but be careful not to let it burn. Remove from heat. Butter a baking dish with 12g/½oz butter and place the cod fillets in it, cover with the fish stock and cook in a preheated moderate oven 190°C/370°F/Gas 5 for 15 minutes. Strain off the fish stock, add to the milk and gradually add this to the saucepan containing the flour and butter. Bring slowly to the boil, stirring gently, to get a smooth consistency.
Sauté the mushrooms in the remaining butter, add to your sauce with 25g/1oz of the cheese and the anchovy essence. Stir until cheese has melted, season to taste. Cut the fish into bite-size pieces. Add the shrimps and parsley to the fish in the baking dish, pour the sauce over the fish shaking the dish gently for the sauce to sink. Place the dish in a preheated oven at 200°C/400°F/Gas 6 for 10 minutes. Sprinkle over the remaining cheese, and put under a hot grill for a few minutes for the cheese to melt and brown.