Combine the trimmed-off fish scraps thoroughly with the milk-soaked, squeezed-out bread roll, the butter, the eggs, and salt, then pass through a sieve to get a smooth paste.
Stir in the finely chopped button mushrooms sautéed in butter.
Grease a roasting pan thickly with butter, and place the salted fillets in it with the side the flesh was trimmed from facing up.
Spread the fish-and-mushroom paste evenly over the top of the fillets.
Sprinkle with a little breadcrumbs, and dot with a few knobs of butter.
Roast in a hot (220°C) oven for 10-12 minutes, until the topping sets, turns lightly golden, and the fish is cooked through.
Cut into slices and arrange on a platter.
Serve with Béarnaise or hollandaise sauce.
Based on: Malatinszky Fanny szakácskönyve (a classic Hungarian cookbook), modernised. Calories and protein are estimated.