Using a sharp knife or mandoline slicer, finely chop the cabbage into thin ribbons.
Using a box grater or food processor, grate the carrot.
Mince the onion; set all ingredients aside.
In a small mixing bowl, whisk together the buttermilk, white vinegar, milk, mayonnaise, lemon juice, sugar, salt and black pepper until smooth and well combined; taste the dressing and adjust seasonings as needed—add more sugar for sweetness or vinegar for tanginess.
Place the chopped cabbage, grated carrot, and minced onion in a large mixing bowl.
Pour the prepared dressing over the vegetables and toss gently until everything is evenly coated; Be careful not to overmix as this can bruise the delicate cabbage.
Cover the coleslaw and refrigerate for at least 30 minutes to allow the flavors to meld together; For best results, chill for 1 to hours before serving.
Scoop the coleslaw into bowls or serve alongside your favorite fried chicken, burgers or sandwiches.
Store leftovers in an airtight container in the refrigerator for up to 3 to 4 days .