Whisk together first 5 ingredients and 1/2 cup blue cheese in a very large bowl. Add green cabbage, carrot, and half of green onions; toss to coat. Just before serving, transfer to a serving bowl, and stir in red cabbage. Sprinkle with remaining blue cheese and green onions.
Recipe adapted from Smoke: New Firewood Cooking copyright by Tim Byres. Published by Rizzoli.