Add olive oil to a large skillet. Set the heat to medium, and let the oil heat-up for a few minutes. When oil is hot, add the whole, cracked eggs one at a time. Lower the heat to medium and cook for a few minutes until the egg whites turn white. Using a spoon, baste the eggs with the hot oil until the tops are cooked with the consistency you desire. You might need to carefully tilt the pan to collect the oil to baste the eggs. Serve immediately, seasoned to taste with sea salt, black pepper and rigani.