Pre-heat to 450 degrees. Peel the potatoes and boil them until very soft. Drain and mash them well. Over low heat saute the onions and parsley in butter.
Meanwhile, grease the sides and bottom of a 10-inch round pan. When the onions are transparent combined onions, parsley, butter, mashed potatoes, salt, and pepper. Beat the eggs and stir them in. Pour the mixture into the greased pan and bake for 20 minutes. When slightly cooled, remove the pan and slice.