Preheat the oven to 425ºF.
Spray a small baking sheet with cooking spray and add the wonton strips. Toss to coat with some of the cooking spray. Spread out evenly. Bake for 5 minutes, or until starting to turn brown and crisp. Remove and cool.
Spray another small baking sheet with cooking spray (or use the same one after wontons are baked) and add the chicken breasts. Drizzle the 1 tbsp soy sauce and 1/2 tsp sesame oil over the 2 breasts. Bake for 15 minutes, or until chicken releases clear juice when pierced with a knife. Remove and allow to cool slightly.
In a large bowl add the romaine lettuce, spinach, mandarin orange segments, mushrooms, and scallions. Toss to combine. Set aside.
In a medium bowl add all of the dressing ingredients (mayonnaise, honey, rice wine vinegar, dijon mustard, grated ginger, toasted sesame oil, and sriracha sauce) and whisk to combine. Drizzle over the greens and toss to coat. Divide between 2 serving bowls and top with sliced chicken breasts and wonton strips. Sprinkle with sesame seeds to taste and serve.