The purpose of the egg in the mixture is to create a binder between the cheese and the pasta. The egg also acts as a thickener for the cheese if the mixture has too much moisture. I seriously considered adding an egg to my mixture. My thought was based on almost always adding a beaten egg. However, I didn't feel like my mixture would be too moist to the point that it would become runny while baking, so I opted not to use the egg.