Bring a pan of water to the boil and cook the potato for 8-10 minutes until tender. Drain the potato and mash it.
Heat half of the oil in a non-stick pan, spoon the potato mixture in and spread evenly. Season with salt and freshly ground black pepper and fry for 4-5 minutes on each side until golden brown.
Fry the haggis slices in a separate pan for 3-4 minutes on each side until golden and cooked through.
Heat the rest of the oil in a small frying pan, crack the egg in and fry for a few minutes, or until set.
To serve, arrange the potato cake on a serving plate, serve the cooked haggis on top and top with the fried egg.