Remove the core from the green and red cabbage and slice both very thinly using a sharp knife or mandoline.

Peel the carrots and grate them coarsely using a box grater.

In a large mixing bowl, toss together the shredded green cabbage, red cabbage, and grated carrot.

In a separate bowl, whisk together the mayonnaise, apple cider vinegar, sugar, dijon mustard, salt, and black pepper until smooth.

Pour the dressing over the cabbage mixture and toss thoroughly until every strand is coated.

Cover the bowl and refrigerate the coleslaw for 30 minutes so the cabbage softens slightly and absorbs the dressing.

Give the chilled coleslaw one more toss and taste, adding a pinch more salt or vinegar if needed.

Transfer the coleslaw to a serving bowl and serve cold as a side.