You now have artichoke hearts. Cut each heart into quarters and trim the inner choke away, then place the quarters in a saucepan with water to cover. Mix in the flour and add the lemon halves. Bring to a boil, reduce heat and cook a few minutes until artichoke quarters are al dente. Remove from heat, drain, discard the lemon and let artichokes cool.
Dice artichoke quarters and set aside.
Lightly saut the onion and garlic in the butter. When softened, add the diced artichokes and cook for a few minutes. Add cream and cook through, until sauce is thickened. Season with pepper. Salt is unlikely to be needed because both broth and Parmesan are salty.