In a large bowl, toss together the kale, apple, cabbage, carrots and onion.
In your blender, combine the ginger, garlic, olive oil, vinegar, lime juice, sesame oil, and sugar. Blend until smooth, then season to taste with salt and cayenne pepper.
Toss the dressing with the kale-apple mixture. Chill until you're ready to serve.
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Notes
For this recipe, choose a firm, sweet apple like Gala, Fuji, Envy, or Honeycrisp. For a saucier slaw, you can double the dressing. You can make this up to a day ahead. Leftovers will keep for 3 to 4 days in a covered container in the refrigerator. Your apples may begin to brown as they sit, but they'll still taste good!