Cook the chopped potatoes in salted water until just tender, about 10 minutes. Drain and cool. Season well with salt and pepper.
Heat the oil in a large frying pan over a low heat and gently fry the onion until soft. Turn up the heat and add the bacon, mushrooms and sprouts. Fry for 5 minutes. Return the potatoes to the pan and cook for a further 5 minutes.
Make 4 wells in the mix and crack the eggs into them. Cook gently until the eggs cook. Crumble with stilton and sprinkle with parsley to serve.