In a nonstick saute pan, heat the oil until just smoking. Drain the artichokes and pat them dry with towels. Saute the artichokes a handful at a time until they are golden brown. Continue until all are done.
Meanwhile, crack the eggs into a bowl and just break the yolks. Do not whisk or stir. Add cheese and let stand. When all the artichokes are done, place them all back in the pan. Pour the eggs over the artichokes and swirl the pan to allow the eggs to drip through and make contact with the pan. Cook until the eggs set, about 5 to 6 minutes. Toss onto a plate and serve.