Pour 1-quart water into a large bowl. Cut a lemon in half and squeeze 1/2 into the water. Add salt. Break off the artichoke stems at the base. Remove the outer leaves, pulling away and downward, to leave the fleshy parts behind. When you reach the inner leaves, cut them off with a sharp knife about 2/3 of the way down. Rub the cut surfaces of the artichokes with the other half of the lemon to prevent discoloring. Pare away the tough outer layer on the bottom of the artichoke, and rub all the cut surfaces with lemon again. Put each artichoke into the bowl of water as you finish with it. Pour the oil into a large saucepan. Add the garlic and artichokes. Strain the liquid, uncovered, for about 20 minutes, so it reduces in volume. Scoop the central leaves and the choke from the artichoke, using your fingers and a teaspoon. Squeeze the juice from the second lemon and mix it with the cornstarch. When the cooking liquid is well reduced, stir the cornstarch mixture into it. Boil the liquid again, stirring constantly, until it thickens. Arrange the artichoke hearts in a serving dish. If they are to be served hot, return them to the pan with the sauce to heat them through before serving. makes 4 servings.