Peel and finely chop the onions, whisk with vinegar, salt and pepper. Cut off the cress and mix in with the marjoram, then vigorously fold in the oil.
Clean and roughly grate the white cabbage. Cook in plenty of boiling salted water for 3 - 5 minutes to taste. Drain well, then add to the prepared marinade. Turn thoroughly, cover and marinate for about 1 hour.
Wash, grate and quarter the apples, remove the cores and cut the quarters crosswise into wedges. Turn in lemon juice and serve with the coleslaw.