In a large bowl, whisk together the mayonnaise, vinegar, sugar, mustard, celery seed, salt, and pepper until smooth and blended. Set aside.
Quarter cabbages and remove core, then cut into thin shreds or use a food processor. Grate carrot using a box grater or food processor.
Add shredded cabbage and carrots to the bowl with the dressing and use tongs to mix together until vegetables are evenly coated. Add the green onions (reserving some for garnish if desired) and toss again.
Cover bowl and chill coleslaw until ready to serve.
Notes
You will need approximately 3 cups of each shredded cabbage, plus 2 cups of shredded carrot.
Coleslaw benefits from chilling, so let rest in the fridge for at least 30 minutes before serving.