Cut the stalk off the artichokes. Cook the artichokes in plenty of boiling salted water with the juice of 2 lemons for about 30 minutes. In the meantime, heat 1/8 litre of water.
Stir in the contents of the bag with a whisk and bring to the boil. Beat the butter into pieces over low heat until it melts. Wash tarragon, chop finely and fold into the sauce.
Serve the artichokes with the sauce. Garnish with tarragon and lemon.