Prepare the vinaigrette. Add all ingredients for the dressing to a medium-sized jar and secure with a tight-fitting lid. Shake vigorously until fully combined. Season to taste and set aside until ready to use (note 1).
Poach the chicken. Bring a large pot of water to a boil over high heat. Add the chicken and return the water to a rolling boil. Remove from heat, cover, and set aside to "poach" (cook) for approximately 20-25 minutes (do not over-cook or the chicken will dry out). Carefully remove the chicken from the pot and set aside to cool before shredding (note 2).
Cook Pasta. Cook the rotini according to package instructions, checking doneness often to prevent overcooking. It is better to have noodles that are slightly undercooked than overcooked and soggy. Drain and rinse thoroughly with cold water (note 3).
Toss the noodles and chicken with half of the vinaigrette. After rinsing and draining the cooked noodles, return the noodles plus the chicken to the pot. Give the Asian sesame vinaigrette another few shakes and pour approximately half of the dressing over the noodles. Mix well to combine (note 4).
Prepare the salad. In a separate large bowl, combine all ingredients for the salad (the cabbage, cilantro, green onions, carrots, Mandarin oranges, chow mein noodles, and fried wonton noodles) (note 5).
Combine and serve. If you know that you will be eating all (or most) of the pasta salad immediately, simply add the chicken and noodles to the salad ingredients, drizzle with the remaining Asian vinaigrette, and mix well to combine. If you think you will only be eating part of the pasta salad, I recommend mixing the chicken and pasta with the salad in individual serving bowls and drizzling with 1-2 teaspoons of vinaigrette. This will help keep leftovers fresh.
Garnish. Garnish with additional cilantro, green onions, or sesame seeds, if desired.