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Prepare the artichokes by trimming them. In a small stockpot, bring 3 quarts of water to a boil. Cook the artichokes in the boiling water for about 20 minutes, or until the outer leaves will pull away easily with a sharp tug. Drain the artichokes and rinse them in cold water.
Cut the artichokes in half lengthwise. Brush them with olive oil, then sprinkle with salt and pepper. Place the artichokes on the grill, cut sides down. Grill them for about 10 minutes, or until the cut sides are browned.
Coat the artichokes liberally with more olive oil, then squeeze the lemons over them.
Serve along with a bowl of kosher salt for sprinkling over the artichokes.