Place the chicken breasts in a medium pot and cover with water by about 1 inch. Bring to a boil over medium-high heat, then reduce to a simmer, cover, and cook for 15-20 minutes until the chicken is cooked through and reaches an internal temperature of 165°F.

Remove the chicken from the pot and set it aside on a cutting board to cool for at least 10 minutes. Once cool enough to handle, use two forks to shred the meat into bite-sized pieces.

While the chicken cooks and cools, prepare the dressing. In a small bowl, whisk together the fish sauce, fresh lime juice, granulated sugar, minced garlic, and sliced chili until the sugar is completely dissolved.

In a large mixing bowl, combine the shredded green cabbage, shredded red cabbage, julienned carrot, chopped mint, and cilantro. Add the warm shredded chicken to the bowl.

Pour the prepared dressing over the salad mixture. Use tongs to toss everything together gently, ensuring the vegetables and chicken are evenly coated with the dressing.

Transfer the salad to a serving platter and garnish with the roughly chopped roasted peanuts. Serve immediately for the crispiest texture, or let it sit for 10 minutes to allow the flavors to meld further.