When you are ready to make the soup, begin by rinsing out the cargo rice in cold water.
Place the rice in the broth and allow it to soak for 20 minutes to a half hour.
While the rice is soaking, add the butter or olive oil to a skillet and cook the chopped leeks at a medium setting until they begin to soften.
After the rice is done soaking, add the leeks, garlic cloves, lemon slices and salt to the stock and rice in the pot.
Turn on the burner to a medium-high setting and bring to a boil.
Simmer for about 20 minutes.
Add the chopped tomato, greens, and chicken meat.
Continue to cook until the rice is tender, about another 10 to 15 minutes.
Add the juice from 1/2 lemon. Stir in, and allow the soup to cool before serving.
You can eat the soup immediately, and it will taste better as leftovers the next day.