Start by preparing your vegetables. Core and thinly shred the green and red cabbage. Do the same with the carrots. If using the apple, chop it into small cubes or thin strips.
In a bowl, combine the mayonnaise, apple cider vinegar, Dijon mustard, lemon juice, and celery seed (if using). Mix until smooth and creamy. Taste it to adjust the seasoning with salt and pepper.
In a large mixing bowl, add your shredded cabbage, carrots, and apple. Pour the dressing over the vegetables.
Using two forks or spoons, toss the veggies and dressing together. Ensure all the pieces are well coated.
Let your coleslaw sit in the fridge for 30 minutes before serving. This allows the flavors to meld beautifully.