Peel and wash the potatoes and cook them in boiling salted water for about 20 minutes. Peel and wash carrots. Cut 4 carrots with greenery into small carrots. Halve the rest of the carrots and cut into slices.
Cook the carrots in boiling salted water for about 10 minutes. Wash, clean and finely dice the cucumber. Wash parsley, shake dry and chop finely. Mix salad cream and yoghurt, season with salt and pepper.
Drain the potatoes and carrots. Cut the potatoes into slices. Carefully mix carrot slices, potatoes, cucumber, parsley and salad dressing in a bowl and leave to stand. Cut the sausages into 3 pieces each and cut them crosswise at each end.
Heat the oil in a pan and fry the sausages in it. Arrange potato salad and sausages on plates. Garnish each plate with a small carrot. Serve with ketchup and mustard.