In a medium bowl, whisk the ¾ cup vegan mayonnaise, 2 tablespoon plus 1 teaspoon white wine vinegar, 1 tablespoon Dijon mustard, 1 teaspoon celery seed, ½ teaspoon sugar, and salt and pepper to taste until completely combined. We don’t like to taste the sugar in our slaw, so we only add enough to cut the acidity of the vinegar and mustard. If it tastes too tangy, add another ½ teaspoon of sugar.
In a large bowl, add the dressing to the 3 cups of shredded green cabbage, 2 cups red cabbage, 1 ½ cups grated carrot, and most (save a bit for garnishing) of the ¼ cup of chopped parsley and toss to completely combine.