Shred 4 cups (12 ounces) green cabbage and 1 cup (3 ounces) red cabbage.You can do so with a sharp knife, mandoline slicer, or food processor with a slicing attachment.
To a large bowl, add the cabbage, 2 medium carrots grated with the large holes of a box grater, and ¼ cup parsley (finely chopped).
To make the coleslaw dressing, whisk together ⅓ cup mayonnaise, ⅓ cup Greek yogurt, 2 tablespoons apple cider vinegar, 2 tablespoons mustard, 1 tablespoon sugar, 1 teaspoon salt, and ⅛ teaspoon black pepper.
Pour the coleslaw dressing over the cabbage mixture and toss until well combined.Serve this immediately for the best crunch, or make it ahead and refrigerate for up to 3 - 4 days.