Peel and chop the potatoes, bring a large pan of water to the boil and boil them for around 15-20 minutes, until tender. Drain and set aside.
Meanwhile, finely chop the onion, garlic and carrot, and shallow fry in olive oil until soft and golden, for 10 minutes or so. Drain and set aside.
Mash the potatoes with the butter and a pinch of salt and pepper, and then stir in the onions, garlic and carrots, mixing well to combine.
Add the nduja to the mash and stir until evenly distributed.
Cut the chorizo into 0.5cm-thick slices, heat the olive oil and fry the chorizo over a medium heat for 2-3 minutes per side, until crispy. You could also cook the chorizo in the oven until crispy, but I like frying it so that I can use the oil to cook the eggs - it definitely adds flavour!
Remove the chorizo from the pan and place onto kitchen towel to allow the excess oil to drain off.
Crack the eggs into the pan and cook them for around 5-6 minutes, until the white is just set, but the yolk remains runny.
To serve, place the nduja hash onto the plate, top it with a fried egg and sprinkle the chorizo crackling on top.