In a blender combine the lime juice, fish sauce, shallot, chiles, sugar and garlic and blend until smooth. Set aside for 15 minutes to allow flavors to blend.
In a medium non-reactive mixing or salad bowl, combine the papayas, carrots, mint leaves and chopped cilantro. Add the dressing and toss to combine thoroughly. Garnish with the cilantro leaves and chopped peanuts. Serve immediately.