Step 1: Prepare your vegetables. Wash and thoroughly dry the cabbage and carrots. Remove any bruised outer leaves from the cabbage, quarter it, and remove the core. Finely shred both green and red cabbage (if using) using a sharp knife, mandoline, or food processor. Peel and finely shred the carrots. Place all shredded vegetables in a large mixing bowl.
Step 2: Make the creamy dressing. In a separate medium bowl, combine the mayonnaise, apple cider vinegar, granulated sugar, Dijon mustard, and celery seeds. Whisk well until the dressing is completely smooth and the sugar has dissolved. Season with salt and black pepper to taste. Adjust sugar and vinegar as desired for your preferred balance of sweet and tangy.
Step 3: Combine and chill. Pour the prepared dressing over the shredded cabbage and carrots. Using a large spoon or clean hands, gently toss the vegetables until they are thoroughly coated in the dressing. Ensure an even distribution. Cover the bowl tightly with plastic wrap and refrigerate for at least 1-2 hours, preferably 4 hours or overnight, to allow the flavors to meld and the cabbage to soften slightly.
Step 4: Serve and enjoy. Before serving, give the coleslaw another gentle toss. Taste and adjust seasonings if needed. Serve chilled as a refreshing side dish for your favorite meals. Store any leftovers in an airtight container in the refrigerator for up to 3-4 days.