First of all clean the artichokes: cut off part of the stalk leaving just 4 or 5 cm; remove the outer, tougher petals; cut off the tip, the external part all the way round the base below the petals, and the outside of the stalk. As you clean them, put them in a bowl of water with the juice of the lemon (also adding the two halves of the squeezed fruit). Now prepare the batter: in a bowl, use a fork to mix the eggs, cheese, grated peel of the remaining half lemon, and a pinch of salt, gradually pouring in the water. Add the flour and stir with a whisk until you have a smooth batter with no lumps. Strain the artichokes, pat them dry, cut them into thin slices and then into small pieces (they need to be finely chopped). Add the pieces of artichoke to the batter along with the chopped parsley and mix everything together well. Heat the oil in a deep frying pan. Add a few spoonfuls of batter at a time and fry the fritters until golden-brown all over. Then remove them using a slotted spoon, and place them on absorbent paper to eliminate any excess oil. Sprinkle with salt and serve them hot and crispy.