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.