In a large bowl, combine the chopped romaine, sliced cooked chicken, cooked rotini, shredded red cabbage, sliced red onion, shredded carrots, roasted almonds, and chow mein noodles; toss to mix.
Season the salad mixture lightly with salt and pepper and set aside while you make the dressing.
In a medium bowl, whisk together vegetable oil, rice vinegar, sesame oil, honey, Dijon mustard, soy sauce, sesame seeds, 1/8 teaspoon salt, and 1/2 teaspoon freshly ground black pepper until smooth.
Pour the dressing over the salad and toss until everything is evenly coated.
Serve immediately or divide the dressing and toss with individual portions as desired.