Slice the cabbage into thin ribbons using a sharp chef knife or a food processor attachment.
Grate the peeled carrots using the large holes of a box grater.
Place the shredded vegetables in a colander and toss with a teaspoon of salt to remove excess moisture; let sit for 30 minutes.
Whisk the mayonnaise, apple cider vinegar, sugar, celery seed, black pepper, and salt in a medium bowl until the dressing is smooth.
Combine the drained cabbage and carrots with the dressing in a large mixing bowl.
Fold the mixture thoroughly until every strand of cabbage is completely coated in the creamy dressing.