Clean red cabbage and cut into fine strips. Heat 1 teaspoon of butter with the five-spice spice mixture in a small saucepan. Steam the red cabbage for about 3 minutes. Add the orange juice, season with salt and pepper and cook the red cabbage, covered, for about 10 minutes.
Heat the burger buns in a preheated oven at 100 degrees (fan oven 80 degrees) until serving. Wash the thyme and shake well dry. Heat the olive oil, the remaining butter (1 teaspoon) and thyme in a non-stick pan. Fry the fish fillets for 2-3 minutes on each side. Season with salt, pepper and lemon juice.
Rinse the cucumber, pat dry and slice into thin slices lengthwise around the core. Rinse the dill, shake dry, pluck the dill tips from the stems and chop roughly. Halve the burger buns. Spread 1 tablespoon of remoulade on the lid and base. Layer the bun bases with red cabbage, carp fillets, cucumber slices and dill. Place the bun lid on and serve.