Place the chicken breasts in a pot and cover with the salted water.
Bring to a simmer, then cover and remove from the heat for 15-20 minutes until internal temperature reaches 165F.
Shred the warm chicken using two forks and spread on a plate to chill for at least 2 hours.
Combine the grated ginger, rice vinegar, hoisin sauce, canola oil, soy sauce, sesame oil, agave, pepper, salt and sugar in a jar.
Shake the jar vigorously until the dressing is smooth and emulsified.
In a large bowl, combine the chilled shredded chicken, napa cabbage, red cabbage, romaine lettuce, carrots, scallions and cilantro.
Pour the dressing over the salad ingredients and toss until evenly coated.
Divide the dressed salad into bowls.
Top each bowl with the crispy chow mein noodles and toasted almonds just before serving.