Preheat the grill to warm. In a shallow dish, whisk the eggs with 2 tbsp of the clarified butter.
Put a good handful of flour on a plate and season lightly with white pepper and salt.
Take the sea trout fillets and coat them with the seasoned flour, then dip them in the egg mixture and finally toss them in breadcrumbs until they are completely covered.
Heat a frying pan until very hot then add 2 tbsp of the clarified butter. Place the breaded fillets in the pan, skin side up for 2 minutes. Turn the fillets over and cook for a further 3 minutes, or until golden brown. Leave the pan on the heat, transfer fillets to a heat-resistant plate, skin side down and place under the grill for 5 minutes.
Halve the bananas, lengthways. Add the remaining clarified butter to the hot pan and place the banana halves in the pan for 5 minutes, turning occassionally to stop them burning.
In a heatproof bowl sitting over a pan of hot water, whisk the lemon juice, butter and egg yolks to a creamy sauce. Season with salt and pepper to taste.
Take the fillets from under the grill and place tomato and lemon slices over the flesh side, alternately and overlapping so they cover most of the fish. Turn the grill up to full and cook the fillets for a further minute.
Serve the trout and bananas together on a plate, covered with sauce.