Finely mince the head of cabbage using a sharp knife or food processor with a shredding disc. It should resemble confetti. Place in a very large mixing bowl.

Finely grate the carrot and add it to the bowl with the cabbage. Toss to combine.

In a separate medium bowl, whisk together the milk and buttermilk. Add the mayonnaise, sugar, white vinegar, lemon juice, salt, and pepper.

Whisk the dressing vigorously until the sugar is dissolved and the mixture is completely smooth and creamy.

Pour the dressing over the cabbage and carrot mixture. Use a large spoon or spatula to fold everything together until all the vegetables are evenly coated.

Cover the bowl tightly with plastic wrap and refrigerate for at least 4 hours, but preferably overnight, to allow the flavors to meld and the cabbage to soften.

Stir the coleslaw well before serving. Serve chilled.