Combine chicken, 4 cups water, and 2 teaspoons salt in large saucepan. Cook over medium heat until water just begins to simmer, about 10 minutes. Cover pot; reduce heat to low; and gently simmer until chicken registers 160 degrees, 12 to 17 minutes.
Step 2
Transfer chicken to plate or cutting board and let cool for 15 minutes. Shred into thin, bite-size strips.
Step 3
Whisk fish sauce, sugar, vinegar, Thai chile, garlic, and salt in large bowl until sugar is dissolved. Add green cabbage, mizuna, red cabbage, bell pepper, cucumber, radishes, chopped cilantro, Thai basil, mint, and shredded chicken and toss thoroughly to combine. Top with cilantro leaves and peanuts. Serve.