01For the chicken stock: Place the chicken and vegetables in a large stockpot over medium heat. Pour in only enough cold water to cover (about 3 quarts); too much will make the broth taste weak. Toss in the thyme, bay leaves, and peppercorns, and allow it to slowly come to a boil. Lower the heat to medium-low and gently simmer for 1 to 1 1/2 hours, partially covered, until the chicken is done. As it cooks, skim any impurities that rise to the surface; add a little more water if necessary to keep the chicken covered while simmering.
02Carefully remove the chicken to a cutting board. When its cool enough to handle, discard the skin and bones; hand-shred the meat into a storage container.
03Carefully strain the stock through a fine sieve into another pot to remove the vegetable solids. Use the stock immediately or if you plan on storing it, place the pot in a sink full of ice water and stir to cool down the stock. Cover and refrigerate for up to one week or freeze. Makes: 2 quarts
04For the soup: Bring 4 cups of stock to a boil over medium heat in a soup pot. Add the lime leaves, chiles, garlic, ginger and lemongrass. Lower the heat to medium-low; cover the pot and gently simmer to let the spices infuse the broth, about 10 minutes.
05Uncover the pot and stir in the chicken, coconut milk, mushrooms, fish sauce, sugar and lime juice. Simmer to heat the chicken through, about 5 minutes. Sprinkle with salt and pepper. Ladle the soup into a soup tureen or individual serving bowls. Garnish with the cilantro. Be careful to avoid chewing the lemongrass, ginger or lime leaves.