Squeeze the juice of half the lemon into a bowl of water large enough to hold the artichokes. Trim the artichokes down to the heart, rubbing the cut surfaces with the lemon half to keep them from browning. Remove the choke, cut the artichokes into small chunks, and then toss the chunks into the acidulated water.
Heat the olive oil over medium-high heat in a 12 to 14-inch saute pan and add the garlic and parsley. Saute for 2 to 3 minutes, then drain the artichoke pieces, and add to the pan. Cook until the artichokes are very tender, about 10 minutes, adding a little water if necessary.
Beat the eggs in a medium bowl with the cheese and salt and pepper, to taste. Remove the pan with the artichokes from the heat, stir in the egg mixture, and return to medium-low heat. Stir the mixture constantly until the eggs are just set. Remove from heat and serve immediately.