Thinly slice the head of green cabbage, red cabbage and julienne the carrots. Chop onions thinly. Place all these ingredients in a big mixing bowl.
In a separate medium-sized bowl, prepare the dressing for Bill Miller coleslaw. Put mayonnaise, salt, pepper, buttermilk, apple cider vinegar, and sugar in the bowl. Whisk it until everything is blended together and becomes a homogenous mixture.
Drizzle the dressing over the cabbage mix and add celery seed to it. Use tongs or a salad spinner to mix all of them together. Cover the bowl with plastic wrap and refrigerate for at least 1 hour before serving to let the flavors blend.
Serve the Bill Miller coleslaw as a side dish or use it to top burgers, sandwiches, tacos, etc.