Wash and slice the leeks. Place the leeks in a pot of boiling water and boil for 2-3 minutes. Strain leeks and set aside.
In a pot or deep pan, heat the olive oil on medium low heat and add the leeks and sauté until leeks are soft (about 6-7 minutes). Note: You do not want to brown them.
Add the dill and the tomato paste and stir a couple of times, than add the rice and about 1 ¼ cup of hot water. Add salt as needed (I added about ½ a teaspoon) and mix well.
Cover the pot with its lid and simmer at low heat for about 20 minutes, until rice is soft. Check regularly and add additional hot water as needed. Turn off the heat and let it sit for 10 minutes with the lid on.
Serve as a main course with a few drops of lemon juice and freshly ground pepper.