When artichokes are plentiful and prices reasonable, consider splurging to make this rich and creamy soup for a special occasion. The soup is enriched with wine and Parmesan Stock, but if you don't have time or ingredients to make the stock, by all means substitute a good-quality chicken stock. The soup can be made a day in advance of serving and gently reheated. For an even more elegant presentation, add fresh crabmeat to the bisque at the final stage.
Fill a bowl with cold water and add the juice of the lemon and the lemon halves themselves. Cut off and discard the bottom 1/2 inch of the first artichoke stem. Peel the remaining stem with a vegetable parer. Bend back the outer leaves at the base of the artichoke, and when the leaves snap, pull down sharply to remove the tough skin. Continue in a circular fashion around the artichoke, removing the bottom 2 or 3 layers of leaves. Cut off the top third of the artichoke and discard. Drop the artichoke in the bowl of acidulated water. Prepare the remaining artichokes in the same manner.
Steam the artichokes until they're tender when pierced with a sharp knife or skewer, 15 to 25 minutes, depending on their size. Remove the artichokes with tongs and set them upside down on a wire rack to drain and cool. When cool enough to handle, remove the leaves and scrape the flesh from each leaf into a bowl. Some leaves will have more "meat" than others. Remove and discard the hairy chokes and small pointed leaves in the center of the artichokes. Cut the artichoke bottoms into slices and add to the bowl with the flesh from the leaves.
Place the oil in a large stockpot and heat over medium heat. Add the onion and cook, stirring frequently, until the onion is tender. Add the garlic and cook another 2 minutes, watching carefully so the garlic doesn't burn. Add the white wine and cook until the liquid is almost evaporated. Add the 4 cups of hot Parmesan Stock, potatoes, and artichokes, and cook, stirring once or twice, until the mixture is heated through. Remove from the stove and let cool for 15 minutes.
Purée the soup with an immersion blender or in a food processor. Strain through a fine mesh sieve into a clean saucepan. Add the heavy cream and gently reheat the bisque until it's hot, but not boiling. If the soup is too thick, thin with remaining Parmesan Stock.
Divide the soup among heated bowls and garnish each serving with a sprinkling of shaved parmesan. Serve hot.