Fill half a medium-sized pot with water, submerge the beef shanks (whole), and set to boil.
Wash 5 lime tree leaves and set aside.
Wash and chop lemongrass stalks into pieces that are 1-2 inches long.
Peel and chop carrot into 1-inch pieces.
Peel and chop papaya into 1-inch pieces.
Place garlic, peppercorns, and cilantro stems into a mortar and pound with the pestle until achieving a paste-like consistency.
Take the beef shanks out of the water, rinse them under cold water, discard the water, and set the meat aside.
Fill half a large pot with water, set to medium heat, then add the carrots, papaya, lime tree leaves, lemongrass, garlic-and-pepper paste, and beef shanks to the pot.
When the soup reaches the boiling point, reduce to low heat and simmer for at least one hour.
Remove the soup from heat and serve over rice.
Garnish the soup with cilantro leaves.