How to Make It
Squeeze the lemon juice into a large bowl of cold water and add the lemon halves. Break off or cut the stem from the base of the artichokes. Using your hands, snap off the tough outer leaves near the base. Continue snapping off leaves until only the central cone of yellow leaves with pale green tips remain. Using a large sharp knife, trim the top cone of leaves to just below the green tips. Trip any tough, dark green areas from the base with a small knife. Cut the artichoke hearts in half. Using a small spoon or a melon baller, scrape out and discard the hairy chokes. Cut each half lengthwise into 4 even slices. Place the artichoke slices in the acidulated water.
In a large nonreactive saucepan, combine 2 tablespoons of the oil with the shallots and a pinch of sea salt and cook over moderate heat, stirring often, until softened but not brown. Stir in the remaining 2 tablespoons oil. Drain and add the artichoke slices and cook until slightly softened, about 2 minutes. Pour the wine all over the artichokes, increase the heat to moderately high and simmer until almost evaporated, about 7 minutes. Add the chicken stock and reduce the heat. Cover and simmer gently until the flavors have mingled, about 20 minutes.
Transfer the soup to a food mill with a fine disk and puree. Discard any fibrous artichoke pieces that remain in the food mill. Return the soup to the pan; you should have about 3 cups. if the soup is too thin, return it to the saucepan and boil until reduced and thickened.
Just before serving, whisk the butter into the hot soup over moderate heat until melted and incorporated. Pour the soup into heated soup plates or bowls and scatter the cheese strips on top. Serve immediately.