Slice the cabbage and onions as thin as possible. This can be done by hand or using a food processor or mandoline. Combine in a large bowl. Grate carrots on a box grater. Add to bowl. Add sugar and salt into the bowl and mix well, massaging the sugar/salt mixture into the slaw mix. Allow to sit for 5 minutes.
After 5 minutes, rinse the mixture well under running water, using a strainer if desired. Repeat 2–3 times. Using paper towels, squeeze mixture to remove remaining water. Add chopped parsley and toss to combine.
In a separate bowl, combine all of the dressing ingredients and mix well. Once combined, stir into salad and toss. Place into fridge and allow to sit at least 3 hours and up to 2 days before eating. This coleslaw is delicious as a barbecue side dish or with the Peruvian Chicken recipe on the next page.