Begin by trimming and peeling off the outer layer of the leeks. Then cut them on a diagonal about 2 inches long and wash them.
Wash and peel the carrots and cut them about 3/4's of an inch wide on the diagonal.
Add the olive oil to a large saute pan (something with a lid) and cook the onions until translucent.
Then add the leeks, carrots, rice and sprinkle the sugar, salt and pepper on top. Pour the water over everything as well as the juice of half a lemon. Cover the pan with the lid and set the flame to somewhere between medium/ medium-low and cook covered for about 20-25 minutes until the leeks and carrots are tender. (Check occasionally if you need to add a little more water. The bottom of the pan shouldn't be dry.)
Transfer everything to a serving dish and drizzle with the 3 tablespoons of olive oil. Serve at room temperature or cold with fresh lemon wedges and chopped parsley and red pepper flakes if desired Enjoy.
*This will keep covered in the refrigerator for 4 days.
*White rice is traditional in this dish, but I try to swap brown whenever I can, and you don't notice the difference here.
*A little more olive oil is generally used for drizzling afterwards so drizzle freely if you desire.
*Some people include 1 or 2 chopped tomatoes in this. My mother-in-law doesn't, so I dont.