Peel and finely chop the garlic. Finely chop enough of the parsley leaves to measure 4tablespoons. Put the garlic and half of the parsley in a heavy-bottomed braising pan with 2tablespoons of the olive oil. Place over medium-high heat and sauté until the garlic begins to sizzle. Lift the leeks out of the water and put them in the pan with ½cup water. Season lightly with salt and cook, stirring occasionally, until the leeks are wilted, about 10 minutes.
Cut the lemon in half. Squeeze the juice from half the lemon into a medium bowl and fill the bowl halfway with cold water. Trim the artichokes as described. Cut them into wedges about ¼ inch thick and put them in the bowl of lemon water to prevent them from discoloring.
When the leeks are done, add the artichokes. Season with salt and pepper and add another ½cup water. Cover the pan, lower the heat to medium, and cook until the artichokes are tender, 10 to 15 minutes, by which time all the water should be evaporated. If all the liquid evaporates before the artichokes are tender, add a little more water.
While the artichokes are cooking, put the broth in a pot over high heat and bring to a boil. Lower the heat to maintain a very gentle simmer.
Raise the heat under the artichokes to medium-high. Add the rice and stir until it is well coated. Add about 1cup of the hot broth and continue stirring. Add only enough broth to produce the consistency of a rather thick soup and wait until all the liquid is absorbed before adding more. Season with salt and continue until the rice is al dente, 20 to 25 minutes.
Remove the risotto from the heat and stir in the remaining 2tablespoons parsley and 1tablespoon olive oil. Serve at once.