Cut top of leeks off, wash, and drain. Cut the white parts of leeks and set a side. Cut the leeks' green parts in half lengthwise and slice them thinly. Wash leek one more time after chopping. Wash, drain, and slice carrots too. Take olive oil,chopped leeks, and carrots in a pot and turn the heat on medium high. Cook it until leek absorbs all of its juice, stirring occasionally.Chop onion and add it into the pot. Stir and cook for 5 minutes. Add 1 cup of boiling water, tomato paste, and rice into the pot and stir. Bring it to the boil. Slice the white part of leeks into 1 inch pieces. Place the leeks' slices on top and cover the lid. Turn the heat down to low and simmer until white leek sileces soft. Turn the heat off. Let it cool. Serve it with pepper flakes and some lemon juice.