Thinly slice the white and red cabbage, or shred them using a large-holed grater.
Grate the carrot as well, then combine with the cabbages in a large bowl.
In a separate bowl, whisk together the mayonnaise, Greek yogurt, apple cider vinegar, brown sugar, mustard, BBQ sauce, salt, and black pepper until you have a smooth dressing.
Pour the dressing over the grated vegetables and mix thoroughly to ensure they are evenly coated.
Cover the bowl and refrigerate for at least 30 minutes to allow the flavors to meld.
Serve chilled alongside grilled dishes, as a topping for burgers, or on its own as a refreshing salad.
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