Remove tough outer leaves of the green and red cabbage, quarter the heads, and remove the dense core. Shred the cabbage into thin, uniform strips.

Place shredded cabbage in a colander over a bowl, sprinkle with salt, and let it sit for 20 to 30 minutes.

Shred the carrots using a box grater.

Rinse the cabbage thoroughly under cold water and dry completely using a salad spinner or clean towels.

In a separate bowl, combine mayonnaise, apple cider vinegar, Dijon mustard, sugar, and celery seeds and whisk until smooth.

In a large bowl, place the dried cabbage and shredded carrots, pour the dressing over them, and toss until evenly coated.

Cover the bowl and refrigerate for at least one hour before serving.