Prepare the white sauce as follows: heat the milk and leave it to the side. In another pot, heat the butter or margarine and then add the flour, stirring constantly. Continue to stir until it has dissolved in the butter. Add hot or warm milk, stirring constantly with a wooden spoon so that it does not form lumps. When the sauce is ready, add salt and pepper.
Remove from the heat and let it cool, stirring occasionally so that it does not form a crust. Add the eggs and 2/3 of the cheese.