Preheat the oven to 450 degrees Fahrenheit. Rinse and dry the chicken breasts, then place them in a single layer in small roasting pan or baking dish. Rub them with olive oil, and sprinkle generously with salt and pepper. Roast for 30 minutes or until the chicken is golden and lightly cooked through. Remove from the oven and allow them to rest for ten minutes or so.
Next, make the dressing. In a small jar or bowl, combine the lime juice, fish sauce, 2 tablespoons of sugar, the water, garlic, and the chili. Whisk well, then taste. If the flavor overwhelms you, add more water, 1 tablespoon at a time. If you would like it more sweet, add more sugar, ½ tablespoon at a time.
Add the mint and basil leaves—you’ll keep them whole—to a bowl with the watercress, but leave out any tough stems. Halve the bell peppers, remove the seeds, and slice them into long, very fine strips. Next, slice the peaches in half, remove the pits, and slice the peaches into thick pieces. Add the bell peppers and the peaches to the bowl with the herbs.
Finally, shred the chicken and its crisp skin. Toss all of the ingredients together with the dressing—add it a few spoonfuls at a time and taste as you toss; you don’t necessarily have to use the whole batch. Let the flavors mingle for a few minutes before serving.