Remove the outer leaves of the cabbages. Finely shred 2 cups each of purple and green cabbage. Julienne 1 cup of orange carrots and chop 1.5 cups of broccoli into small florets. Finely slice 1/4 cup of green onions. Combine in a large mixing bowl.

In a separate small bowl, whisk together the soy sauce, rice vinegar, toasted sesame oil, freshly grated ginger, and honey until smooth. Slowly drizzle in 2 tablespoons of neutral oil while whisking continuously to create an emulsion.

Pour the dressing over the vegetable mixture in the large bowl. Toss thoroughly to ensure everything is well-coated with the dressing.

Transfer the salad to a serving bowl and garnish with toasted white and black sesame seeds and remaining green onions before serving.