For the stock: Put all the ingredients into a large pot and cover with water by 1-inch. Bring to a boil, skimming any foam that rises to the surface. Reduce the heat and simmer for 30 minutes. Remove the chicken and save it for another meal; strain the stock. Makes 10 to 12 cups.
For the soup: Put the Asian Chicken Stock into a pot over medium-high heat. Add the mushrooms, limes, chiles, fish sauce, and kaffir lime leaves, if using. Taste and adjust seasoning with salt. Add the shrimp and simmer just until the shrimp are cooked through, about 5 minutes, then add the cilantro and basil leaves. Taste and adjust seasoning. Serve garnished with cilantro leaves.
Recipe courtesy of Tyler Florence