Remove and discard leek roots and any yellowed tough ends. Cut leeks into one inch lengths, place in a large bowl and rinse in cold water. Drain, rinse and wash leeks in this manner two or three times to remove sand, then leave in a bowl of cold water until ready to add to saucepan.

Heat olive oil in a wide saucepan, add onions and sauté them ten minutes, stirring, until they are transparent but not brown. Add the leeks, carrots, seasonings and water, bring to the boil and add rice.

Lower flame and cook the leeks twenty to twenty-five minutes until the water is absorbed and rice is tender. Cool to room temperature before serving.