For the artichoke puree, slice the lemon and place in a large enough bowl of cold water. Break off stems and lower, outer leaves from artichoke hearts.
Cut upper artichoke halves horizontally small to just above bottoms. Chop green leaf bases to light center. Remove all hay with a spoon; immediately place bottoms in lemon water.
Peel the potatoes. Drain artichoke hearts. Cut both into coarse pieces and bring to a boil in a saucepan with 750 ml water, olive oil and salt. Cook over medium heat until tender, about 20 minutes.
Lift out potatoes and artichoke hearts with a sieve scoop and puree in a food processor with a cutting blade, not too fine.
Add 50 ml artichoke water and the whipped cream. Season the puree with salt and nutmeg, place in a saucepan and heat while stirring. Add the parsley and serve the artichoke puree.