This colorful, piquant slaw is made with an assortment of vegetables and herbs commonly used in Asian cuisines. If you don't feel like chopping all the vegetables by hand, use the grater attachment on your food processor.
Make the dressing: In a medium bowl, whisk together mayonnaise, sesame oil, vinegar, chili sauce, lime juice, ginger, salt, pepper, and sesame seeds; set dressing aside.
Make the slaw: Core the red and napa cabbages, quarter, and slice very thinly. Transfer to a large bowl. Fill bowl with cold water to cover cabbage. Swish cabbage around with hands so any dirt settles to the bottom of the bowl. Lift cabbage, and transfer to a colander to drain. Place in large bowl; set aside.
Using the large holes of a box grater, grate the turnip, daikon, and carrot. Add to bowl of cabbage along with scallions, red bell pepper, mint, and cilantro. Add reserved dressing, and toss to combine. Cover with plastic wrap, and let sit at least 2 hours in the refrigerator, but preferably overnight. Serve chilled. Will keep in refrigerator for up to 4 days.