Wash and clean the leek and cut into fine rings. Peel the carrots and grate finely.
Heat the butter in a pan, sprinkle the leek and carrots with the sugar and cook for about 8 minutes. Stir 2 teaspoons of cream cheese into the vegetable mixture and season with salt and pepper.
Brush the baguette slices with the remaining cream cheese, then top with the vegetable mixture. Cut trout fillets into pieces, place on top. Garnish with cream horseradish, fresh dill and chives.