If you are going to have potato with your English breakfast, hash browns are probably the best way to do it. I've always found commercial hash browns to be bland and flavourless, but if you take the time to make your own, you'll be in for a surprise!
Peel and chop the potatoes into chunks. Put them in a pan of boiling salted water and simmer for about 20 minutes until tender. Drain the potatoes and allow them to cool down completely.
Peel the half onion and chop it as finely as you can. Press the potatoes through a grater and place them in a bowl along with the chopped onion and the salt and pepper. Beat the egg in a small bowl and carefully fold it into the potato mixture - you don't want to mash the potatoes.
Form the potato mixture into triangular patties and put them in the fridge for at least half an hour.
In a large frying pan on low heat, warm up some flavoursome fat - duck, goose, bacon or sausage fat or pork dripping are all good. Gently place the hash browns in the pan and let them cook for about 6 minutes each side. Don't mess about with them too much or you may break them.