1. Fill a medium pot with enough water to cover the chicken by 2 inches. Add the salt to the water. Bring to a boil, then turn down the heat to just below a simmer. Place the chicken in the water, making sure the water does not boil so that the chicken stays tender. Once the chicken reaches an internal temperature of 150 degrees F or is firm and white in the center (not pink), remove from the pot and set on a plate to cool. Then cut into 1/2-inch cubes.
2. In a salad bowl, combine the romaine, iceberg lettuce, carrot, and cilantro.
3. To prepare the "wok"-style peanuts, in a medium skillet over medium-high heat, add the peanut oil, peanuts, sugar, and chile flakes. Stir occasionally until the peanuts have small char marks on them but are not burned, 2 to 3 minutes. Transfer to a plate to cool.
4. In a small bowl, whisk together the rice wine vinegar, orange juice, ponzu, soy sauce, and sesame oil until well combined. Adjust the seasoning to taste. Toss all the ingredients together with the dressing and serve.