Finely dice the cabbage until the pieces are roughly the size of rice grains. Use a food processor for a few quick pulses to save time, then grate the carrot and mince the onion into very small pieces.
In a separate bowl, whisk together the mayonnaise, granulated sugar, whole milk, and buttermilk until the sugar is fully dissolved. The dressing should be thin, sweet, and creamy.
Add the lemon juice, white vinegar, salt, and black pepper to the dressing. Stir well to ensure the acidity and seasoning are perfectly balanced before mixing it with the vegetables.
Pour the dressing over the chopped cabbage, carrots, and onions in a large bowl. Use a spatula to fold the mixture together until every piece of vegetable is thoroughly coated.
Cover the bowl tightly and refrigerate for at least four hours, or ideally overnight. This allows the cabbage to soften slightly and the flavors to develop into that signature restaurant taste.
