Clean the cabbage, wash it, quarter it and remove the stalk. Slice or cut cabbage into very fine strips. In a large bowl, knead well with 1 teaspoon salt and 1 teaspoon sugar. Dice plums very finely and fold in.
Peel and chop the onions. Heat the oil in a pan. Fry the onions in it until transparent. Deglaze with vinegar, bring to the boil and simmer for about 1 minute. Season well with 2 teaspoons of sugar, salt and pepper. Pour the onion mixture over the cabbage. Mix everything well and let it stand for about 2 hours.
Coarsely chop the nuts and roast them if necessary. Fold into the salad before serving. Season to taste again.