Patient cooking will bring wonderful results. Spooning a little chicken broth into the oil during the initial cooking helps the artichokes cook evenly. If is important to get small artichokes, with crisp, not rubbery leaves. They are found at the peak of artichoke season, March and April.
Prepare artichokes: Add ¼ cup white wine vinegar to a large bowl half-filled with cold water. Cut a lemon in half and keep it close at hand.Spread open the artichoke leaves to reveal the curly violet inner leaves which surround the choke. Carefully pull these out. With a teaspoon, scrape out the hairy choke, making sure not to dig into the artichoke heart. Work quickly and rub the lemon halves over the cut surface as you work, to prevent darkening.
Spread leaves apart and press each artichoke against a flat surface to bend the leaves back. The artichoke should look like a partially opened rose. Sprinkle salt and pepper between the leaves.
Heat the oil and broth to simmering over low heat in a heavy large Dutch oven or pot (not aluminum) with a tight fitting lid. The pot should be large enough to hold the artichokes side by side, with enough room to turn them during cooking. Place the artichokes in the pot stem side up. Cover and simmer 10 minutes, checking to make sure the broth has not boiled away. If it has, add a couple of tablespoon of broth and replace the cover.
Remove the cover and reduce the heat to very low. Turn the artichokes stem side down. Sprinkle with salt and pepper. Cook, turning every 5 minutes or so, until hearts and bottoms are tender, about 35 minutes. Every time you turn the artichokes stem side up, press them gently with a wooden spoon to spread out the leaves. Transfer to a serving plater, stem side down, taste and sprinkle with salt and pepper, if necessary, and drizzle with olive oil.