Poach chicken breasts in a medium pot so they are just covered with water. Heat water until it’s steaming, but not quite simmering. Cover and let sit on low heat until chicken is just cooked through. They should take about 20 minutes to poach. Try not to overcook them or they will dry out. Once cooked, remove chicken breasts, cool, and shred with forks.
For dressing, combine jalapeño (seeded) and garlic in a small food processor with lime juice. Pulse until minced. Then add other ingredients and pulse until combined.
Chop bok choy, red pepper, cucumber, and grate carrot. For papaya, cut in half and remove seeds (you can eat the seeds, but I don’t love them). Peel papaya and slice thin. Toss veggies and fruit with bok choy. Drizzle with a few tablespoons of dressing.
Add pulled chicken and thawed edamame. Garnish with a handful of fresh cilantro and mint and an extra drizzle of dressing. Serve extra dressing on the side.
If you’re planning on storing some of this salad for later, don’t dress it until you’re ready to serve it. The dressing will start to pickle the ingredients a bit so just store them separately until you are ready to serve them.