In a large mixing bowl, whisk together the mayonnaise, granulated sugar, apple cider vinegar, Dijon mustard, salt, and black pepper until the sugar is fully dissolved and the dressing is smooth.
Add the shredded green cabbage, shredded red cabbage, julienned apple, dried cranberries, and chopped red onion to the bowl with the dressing.
Using salad tongs or two large spoons, gently toss the slaw until all ingredients are evenly coated with the dressing, being careful not to bruise the apple pieces.
Cover the bowl with plastic wrap and refrigerate the coleslaw for at least 30 minutes to allow the flavors to meld and the cabbage to slightly soften.
Before serving, give the coleslaw one final toss to redistribute the dressing and check seasoning, adding more salt or pepper if desired.