Wash and shred the cabbages.
Wash and grate the carrots.
Put all the shredded and grated vegetables in a large bowl.
In a medium bowl, mix the mayonnaise, vinegar, sugar, parsley, celery salt and ground pepper together thoroughly with a whisk.
Add the dressing to the shredded cabbages and grated carrots and toss thoroughly.
Cover and place in the fridge for at least two hours or overnight.
Toss again before serving.
Store leftovers in the fridge.