Preheat the oven to 375 degrees F. In a 10-inch, ovenproof skillet, heat the olive oil over high heat until almost smoking. Drain the artichokes and pat dry, then add to the pan with the garlic. Cook over high heat 5 to 8 minutes. Set aside. In a medium bowl, beat the eggs until frothy, then add the parsley, flour, salt and pepper to taste and the cheese and mix well to combine. Pour this mixture over the artichokes in the pan and return to the stove, cooking 4 to 5 minutes over medium heat to let the bottom set. Transfer to the oven and cook 15 to 20 minutes, until the edges set and the top begins to brown. Cut into wedges and serve.