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Heat the oven to 200C/180C fan/gas 6. Tip the grated potato into a clean tea towel and wring out any excess water. Transfer to a bowl and mix in the beaten egg, flour, cheese and half the spring onions. Season with plenty of salt and a grinding of black pepper.
Brush a 20cm ovenproof skillet or frying pan with the oil and set over a medium heat. Once hot, press the hash brown mixture into the pan using the back of a spoon, making a well in the middle. Fry for 6-8 mins until golden.
Transfer the hash brown to the oven and bake for 10 mins. For the toppings, break the egg into the gap and sprinkle the cheese over the hash brown. Bake for 8-10 mins until the potato is crisp and the egg white is set and the yolk runny (or cooked the way you prefer). Sprinkle over the remaining spring onions and the chilli flakes, if using.