Combine beaten eggs with pasta, Parmesan and season to taste. Heat half the butter in a large non-stick fry pan. Pour in pasta mixture. Cook over moderate heat, without stirring, for 4-5 minutes, or until the bottom is golden brown. Loosen the frittata by shaking the pan backwards and forwards.
Gently flip the frittata, downside up onto a plate. Melt remaining butter and slide frittata into pan and continue cooking until golden brown on the second side, 3-4 minutes more.
The frittata can be served hot, at room temperature, or cold. Cut into 4 wedges. Serves 4.