Thinly slice each artichoke half. Return the slices to the lemon water. Heat 2 tablespoons of the olive oil in a heavy, wide-based pot (like a Dutch oven) over medium-low heat. Add the leeks and garlic and cook, stirring occasionally, until the leeks are soft, about 10 minutes. Drain the artichokes and add them to the pot; season with salt and stir to coat. Cover and cook until the artichokes are tender, about 15 minutes, checking to be sure they're not burning (a little browning is good).

Meanwhile, put the broth in a medium saucepan and bring to a simmer. Adjust the heat to keep the broth at a bare simmer.

Add the rice to the artichokes and cook, stirring for 2 minutes. Add enough broth to cover the rice and simmer gently, stirring often and adding more broth, 1/2 to 3/4 cup at a time, when the previous addition has been absorbed. (You may not need to use all the broth, or you may need a little more.) After 18 to 20 minutes, when the rice is just al dente, cover the pot and remove it from the heat. Let stand 3 minutes, uncover, and stir in the remaining 2 tablespoons olive oil, the parsley, lemon zest, and several grinds of pepper. Taste and adjust the seasonings, adding more broth to loosen the risotto if you like. Divide among warm bowls and serve immediately.