In a small bowl, whisk together the rice vinegar, garlic, and ginger until combined. Add brown sugar, sriracha, and hot mustard, mixing thoroughly. Gradually drizzle in both oils, whisking continuously until emulsified and smooth.

In a large bowl, combine romaine lettuce, red cabbage, carrot, green onions, almonds, and mandarin oranges. Gently fold in cooked chicken, followed by wonton strips and sesame seeds.

Pour the prepared dressing over the salad mixture and toss gently to coat.

Serve immediately in a large bowl or plated individually, garnished with additional sesame seeds.