Rinse trout fillets, dab dry and cut diagonally into thin slices. Place between cling film and beat 1-2 mm thin. Arrange the fish slices on two plates.
Clean, wash and finely dice the fennel. Keep the fennel green. Heat 2 tablespoons of oil in a frying pan. Sauté the fennel for 1-2 minutes while stirring. Season with salt and pepper.
Wash parsley and shake dry, pluck the leaves and cut into strips. Mix lemon juice and 3 tablespoons of oil. Mix in the fennel, capers, parsley and fennel greens. Season with salt, pepper and 1 pinch of sugar.
Drizzle the dressing over the trout carpaccio. Slice the parmesan into thin shavings with a peeler. Sprinkle trout carpaccio with Parmesan. Baguette tastes good with it.