In a quart sized mason jar, combine all of the dressing ingredients.Reach a fork into the jar and give it a swirl to get the brown sugar lifted from the bottom of the jar. Lid the jar tightly and shake to dissolve the sugar and combine evenly. Set aside.
In a very large mixing bowl, toss together all of the salad ingredients with your hands or a pair of tongs. Shake the jar of dressing vigorously to recombine, pour over the salad, and toss to coat. Sprinkle with toasted sesame seeds and serve immediately. Leftovers can be stored in a tightly lidded container for up to three days in the refrigerator.