Pop the cubed potato into a medium saucepan. Fill with water, add a pinch of salt and bring to the boil. Boil the potato for around 7 minutes - or until soft (the exact time will depend on the size of your potatoes). Drain and leave to steam dry.
Meanwhile, drizzle a little of olive oil into a medium-sized non-stick frying pan and place over a medium heat. Add the onion and pepper and fry for about 10 minutes, stirring often, until softened and caramelised. Remove from the pan and tip into a bowl.
Return the pan to the heat and add the chorizo. Fry until the fat has rendered down and the chorizo has turned crispy. Remove from the pan and place into the bowl with the vegetables, leaving behind the oil (which should have infused with the smoky chorizo flavour).
Add the potato cubes to the pan with the chorizo oil and another drizzle of olive oil. Season with salt and fry over a medium heat for about 3-4 minutes, turning regularly to avoid sticking, until the potatoes are crispy on the outside.
Return the onions, peppers and chorizo to the pan and fry for a further few minutes, stirring everything together.
In a separate small non-stick frying pan, add a drizzle of oil and place over a medium heat. Once hot, add the egg and fry until the edges are crisp but the yolk is still runny.
Tip the hash onto a plate, top with the perfectly fried egg and sprinkle with freshly chopped parsley. Serve with lemon wedges on the side to squeeze over the juice. Enjoy!