Add the shredded cabbage and carrot to a large mixing bowl.
In a separate small bowl, whisk together the mayonnaise, sugar, apple cider vinegar, yellow mustard, salt, and pepper until smooth.
Pour the dressing over the cabbage mixture.
Toss well until the cabbage and carrots are evenly coated. At first, it may look like there is not enough dressing, but keep mixing. The cabbage will soften slightly as it sits and the dressing will spread.
Cover and refrigerate for at least 1 hour before serving.
Stir again before serving.