Begin by shredding the green and red cabbage using a sharp knife or a food processor for uniform pieces. Next, peel and shred the carrots. Finely chop the broccoli into small florets and slice the green onions. This preparation should take about 10 minutes.

In a medium bowl or jar, combine the rice vinegar, soy sauce or tamari, honey or maple syrup, toasted sesame oil, and neutral oil. Add grated ginger, minced garlic, and the juice of one lime. Whisk or shake until smooth and well-combined. This should take about 5 minutes.

In a large mixing bowl, add the prepared shredded green and red cabbage, shredded carrots, chopped broccoli, and sliced green onions. Pour the freshly made sesame dressing over the veggies, and toss gently until evenly coated. This mixing should take about 2 minutes.

Before serving, sprinkle the crispy chow mein noodles or fried wonton strips on top for added crunch. Finish with sesame seeds. This enhances appearance and texture.

Serve immediately for best texture, refrigerating dressed slaw without toppings for up to 3 days. Add toppings before serving.