1. Combine 8 cups water and chicken leg quarters in a Dutch oven. Bring to a boil, skimming and discarding foam as needed. Reduce heat to low.
2. Trim and discard root end of lemongrass stalks; discard toughest outer leaves. Smash stalks with the flat side of a knife. Add lemongrass, ginger, garlic, and peppercorns to pan. Partially cover, and simmer 50 minutes, skimming and discarding foam as needed. Remove chicken from pan using a slotted spoon; reserve for another use.
3. Strain broth through a cheesecloth-lined colander; discard solids. Cool to room temperature. Cover and chill for 8 hours or overnight. Skim solid fat from surface; discard.
4. Heat the broth in Dutch oven over medium heat, and stir in salt. Sprinkle with cilantro leaves.