For the dressing: Whisk together the mayonnaise, miso, lemon juice, mustard, Worcestershire and garlic in a medium bowl. While continuing to whisk, slowly drizzle in the oil until smooth and glossy. Add the Parmesan and stir just to combine. Season with salt and pepper.
For the salad: Toss together the romaine, napa cabbage and red cabbage in a large bowl. Pour half the dressing over the salad and mix with tongs to coat. Taste the salad and add more dressing if you like; store the remaining dressing in an airtight container in the refrigerator.
Transfer the salad to a serving bowl, top with the crispy wontons and serve immediately.