Place chicken, lemongrass, scallions, onion, sliced ginger, chile, peppercorns, and water in a large pot. Cover, and bring to a simmer. Uncover partially, and gently simmer for 1 hour.
Add cilantro and mint stems, and simmer for 15 minutes. Add fish sauce, and strain through a cheesecloth-lined sieve. Reserve broth and chicken. Discard remaining solids. Shred chicken meat, and discard bones. Refrigerate broth and chicken separately for at least 4 hours (or overnight).
Skim fat from broth, and reheat broth. Combine chicken, julienned ginger, cilantro leaves, thinly sliced mint, and bean sprouts in a bowl. Divide broth among bowls, and serve with chicken mixture on the side.
In Chinese cultures, lemongrass and cilantro are considered yin ingredients -- cooling elements that are ideal on hot days.