If making your own shredded chicken, simmer boneless thighs in broth or water until tender, then shred with two forks. Set aside to cool.
In a large bowl, combine romaine, Napa cabbage, red cabbage, carrots, edamame, shredded chicken, and crushed wonton strips.
Gently toss to mix the bulk ingredients evenly.
Fold in mandarin oranges, scallions, and sliced almonds to avoid bruising delicate components.
In a mason jar or bowl, whisk together grapeseed oil, sesame oil, apple cider vinegar, soy sauce, brown sugar, ginger, garlic, chili garlic sauce, salt, and pepper.
Secure the jar and shake vigorously to dissolve sugar and emulsify the dressing.
Drizzle the dressing over the salad and toss to coat evenly.
Serve chilled or at room temperature. Store leftovers in an airtight container in the fridge for up to 5 days.