Make the potatoes, then peel and cool.
Cut the cabbage in half, remove outer unsightly leaves and the stalk.
Slice or shave the cabbage very thinly. Mix half of the shaved cabbage with 2 tbsp apple cider vinegar and 3 tbsp sunflower oil or other vegetable oil. Finely chop the caraway seeds and stir them in. Season the cabbage salad with salt and freshly ground pepper to taste.
Peel and finely grate the carrot, chop the remaining shaved cabbage a little more and mix with grated carrot. For the mayo, mix 1 tsp mustard, 1 tsp vinegar and the egg yolks. Slowly add sunflower oil or other vegetable oil while stirring until the mayo has the desired consistency.
Season with pepper and salt. Mix the cabbage and carrot with the mayo, perhaps seasoning with a pinch of sugar.
Slice the potatoes into shavings. Grate cheese, chop chives.
Heat clarified butter in a frying pan and spread half of the potatoes evenly on the bottom of the pan. Sprinkle cheese and half of the chives on top. Cover with the remaining potato chips all together, do not squeeze the potatoes, overall the hash should remain loose. Roast until golden brown on both sides. Season with salt and pepper.
Season the slaw again and stir in remaining chives.
Cut Rösti in half and serve with both salads.
Tip: As an alternative to the fresh chives, you can also use the freeze-dried ones.