Make the dressing: In a medium bowl, whisk together the vegetable oil, vinegar, peanut butter, soy sauce, sesame oil, mustard powder, lime juice, honey, sesame seeds, ginger, and garlic. Season with salt and black pepper and set aside.
Step 2
Make the salad: Into a small heavy-bottomed pot fitted with a deep-fry thermometer, pour the oil to a depth of 2 inches. Turn the heat to medium-high, and when the temperature reads 350˚F, add the wontons. Cook, stirring occasionally, until the strips are crisp, 20–30 seconds. Using a slotted spoon, transfer to a paper-towel-lined plate.
Step 3
In a large bowl, toss together the chicken, cilantro, cabbage, and lettuce. Divide the salad among 4–6 serving bowls, then top evenly with the sprouts, peas, scallions, carrot, cucumber, and bell pepper. Drizzle with the dressing, sprinkle on the chile if using, and garnish with the sesame seeds, peanuts, and wonton strips.