Wash the salmon fillet, dab dry and remove any bones. Cut fillet into 12 slices. Wash the limes hot, dab dry and finely grate the skin. Squeeze the juice. Wash the dill, shake dry and cut finely.
Rub the salmon slices with pepper, lime zest and half of the dill. Cover and chill for at least 30 minutes.
Preheat oven (electric cooker: 200 °C/circulating air: 175 °C/gas: level 3). Peel and wash the potatoes and slice them into thin slices. Layer the potatoes in flakes in a gratin dish. Season the individual layers with salt and pepper.
Mix cream and horseradish and pour over the potatoes. Bake in the oven for 40-50 minutes.
For the cucumber salad, peel and finely dice the onion. Wash parsley, shake dry and chop. Mix vinegar, some salt, pepper and mustard. Fold in the oil. Add parsley, onion and the rest dill.
Season to taste with sugar. Wash the cucumber, peel if necessary and slice into thin slices. Mix with the vinaigrette.
Place the potato gratin on the lowest rail of the oven about 15 minutes before the end of the cooking time. Place the salmon slices on a baking tray. Sprinkle with lime juice and season with sea salt. Spread butter as flakes on top.
Cook in the oven at the same temperature for 10-12 minutes. Arrange everything. Add the cucumber salad.