Boil water and cook pasta to al dente. Drain and set aside.
Mix egg in a small bowl and set aside.
Melt butter and mix in flour. Stir until browned and add milk in small amounts to form a thick but still pourable roux. Add about ½ of the cheese and stir to melt and thicken. Save the rest.
In another bowl, mix together the pasta, cheese sauce, and some of remaining cheese, reserving some for topping.
Put pasta into a buttered casserole dish. Sprinkle a thick layer of shredded cheese on top. Bake at 375 for 30 minutes, until top is crisp and browned.
Cool and enjoy!