A lot of the videos trying out the meal indicated that the easiest way to grate the egg was to wait for it to cool, rather than trying it immediately when it's warm and softer.
Grating a cold egg, and I don't say this lightly, was one of the most gag-worthy cooking experiences I've had and it unleashed an egg odor that lasted all evening.
Once the egg was fully grated, it almost looked like I had sprinkled cheese on my toast but as I would learn when I tucked in, that would have been a tastier option.