Using a sharp chef's knife or a mandoline slicer, finely shred the vibrant purple cabbage and the pale green cabbage. Rinse gently under cold water and pat completely dry with paper towels.

Peel the carrots and slice them into thin, julienned matchsticks. Cut the raw broccoli into very small, bite-sized florets. Add them to the dried cabbage.

In a small glass jar, combine the toasted sesame oil, rice vinegar, soy sauce, honey, neutral oil, and fresh grated ginger. Shake vigorously until it becomes a glistening, semi-translucent golden-brown sesame-ginger dressing.

Pour the emulsified dressing evenly over the vegetables in a large mixing bowl. Toss continuously for 60 seconds until the ingredients are tightly intermingled and evenly coated.

Transfer the salad into a large shallow matte white ceramic bowl. Scatter the toasted white sesame seeds, black sesame seeds, and chopped fresh green scallions over the top. Serve immediately.