Shred the cabbage into thin slices. You can do so with a sharp knife, mandoline slicer, or food processor with a slicing attachment.
To a large bowl, add the cabbage, carrots grated with the large holes of a box grater, and finely chopped parsley.
Make the coleslaw dressing by whisking together ⅓ cup vegan mayo, ⅓ cup Greek yogurt, 2 tablespoons apple cider vinegar, 1 tablespoon mustard, 1 tablespoon sugar, 1 teaspoon salt, and ¼ teaspoon black pepper.
Toss cabbage with dressing and serve.
