Bring a large pan of salted water to the boil with the lemon halves. Cut the stalk off the artichokes. Drop them into the water and boil for 40-45 mins.
Dice the butter. Pour the wine into a pan, reduce by half, reduce heat and whisk in the butter one small piece at a time. Whisk in the Parmesan and lemon juice.
To eat, pull off the leaves, dip the broken end into the sauce, eat this and discard the rest. When you reach the middle, lift out the central leaves, scrape away the hairy choke and eat the artichoke heart.