Whisk the lime juice, fish sauce, 1 tablespoon of the soy sauce and brown sugar in a large bowl until the sugar dissolves. Add the cilantro, scallions and chiles; set aside.
Heat the chicken stock in a large skillet over medium heat until steaming but just below a simmer. Add the pork and the remaining teaspoon soy sauce, and cook, breaking into pieces with a spoon (not too small), until the meat is just cooked through and no longer pink, about 6 minutes. Add the ginger and garlic, and remove from the heat. Combine the chicken mixture with the lime mixture until well coated. Let sit for at least 15 minutes while the flavors combine.
To assemble, put 1 to 2 tablespoons of the chicken filling in the center of each lettuce leaf. Top with chopped peanuts, shredded carrots and chopped cilantro. Strain the remaining liquid from the filling, and serve on the side.
Copyright 2015 Television Food Network, G.P. All rights reserved.