In a large saucepan toss the leek and carrot slices with the olive oil. Cook over medium heat for 5 minutes, until the vegetables are lightly browned, then stir in the remaining ingredients. Cover the pan and simmer the mixture for 1 hour, until the lentils are tender and most of the liquid has been absorbed.
To keep the leek slices intact, do not stir.
Serve hot.