Shred the cabbage to get shreds as thin and as long as possible. You could also chop it if you prefer it that way. Peel and shred the carrots. Chop the green onions as fine as possibly, by hand. Toss all the vegetables together in a big bowl.
Mix all the dressing ingredients together, whisking to blend as each is added. Pour about half the dressing over the vegetables, and add enough more to coat but not to make a puddle of dressing in the bottom of the bowl.