Set up a bowl of cold water and cut up and squeeze one of the lemons into it.
Trim the artichokes by breaking off the stem, and cutting about an inch off of the top. Pull the leaves away working from the bottom til you get to the yellow green portion. Cut in half and put in the lemon water.
Heat the deep fryer to about 250 and once hot, remove the artichokes and dry carefully. Fry them until they start to turn a bit brown around the edges.
Fix the mayo with the other ingredients except the chopped parsley and lemon zest. When ready to serve, and it can be a day later, refry in hotter oil, about 375 until golden. It only takes a few seconds or so. Watch carefully!
Drain on paper towels and dust with good sea salt, pepper and the parsley.
Add the lemon zest in part to the artichokes, with the rest on the mayo and serve with napkins because people will lick their fingers.