Cut artichokes in half, then slices, and fry quickly in medium hot oil until slightly browned. Drain in paper towels.
Season eggs with salt, pepper, nutmeg, and beat lightly. Mix cheese, parsley, and fried artichokes and mix well.
Heat nonstick pan and pour in egg mixture, cook over low heat with lid on until bottom is set.
Place under hot broiler and cook the top of omelette.