Make the dressing by mixing the brown sugar and water together in a small bowl. Stir until the sugar is dissolved. Add the chiles, garlic, lime juice, and fish sauce. Add Kosher salt to taste.
Add the coconut to a small saucepan and place over a medium high setting dry – with no liquid or fat. Stir frequently until the coconut is a golden brown. Remove from heat and set the coconut aside.
Heat the oil, using the same saucepan. Add half the shallot and saute until crisp and golden brown. Remove from the pan and drain, sprinkling with salt. Set aside.
Now add the peanuts to the pan and toast until they are a golden brown color. It should take about 2 minutes. Remove from the pan and drain. Set aside.
Add the chicken to a larger saucepan and cover with water. Poach over a medium setting until the chicken is only just cooked, or about 10 to 15 minutes. Remove from the liquid and shred the chicken into a large bowl.
Peel the pummelos with a sharp knife and cut the flesh from the membranes. Add the pummelo flesh to the chicken.
Cut the shrimp in half and clean. Sprinkle with salt. Fry the shrimp in vegetable oil until well done. Remove from the pan and drain.
Arrange the cilantro and remaining shallots to a large serving plate and toss with half the dressing.
Add the coconut, peanuts, and dried shrimp, tossing to coat.
Divide the salad among six plates if it is a first course, or three plates for a main course. Now, divide the chicken, pummelo, and shrimp among the plates.
Drizzle the remaining dressing over the salad plates and top with fried shallots.