To make the stock, remove the roots and tops of the leeks and wash thoroughly, removing outer layers as necessary. Cut each leek in half, and then cut each half lengthwise. Wash the carrots, remove their tops, and cut them in half lengthwise.
Put the water in a large saucepan and add the leeks, carrots, peppercorns, and chicken legs. Tie the thyme, bay leaf and parsley stalks together in a bundle with cooking string to make a bouquet garnish and add that to the other ingredients in the saucepan.
Bring to the boil and remove any scum, and then simmer with the lid on for 2 hours.
In the meantime, thoroughly wash the remaining leeks, remove the roots, and slice the white and pale green parts thinly. Wash the carrots and dice.
Strain the stock and discard the solids. Return the broth to the pot.
Add the sliced leeks, diced carrots, and rice to the broth. Simmer until the rice and vegetables are tender, about 20-25 minutes.
Shred the chicken from the legs and add it to the soup.
Add the prunes or apricots and simmer for another 5 minutes.
Season with salt and pepper to taste. Garnish with parsley before serving.