Mix the mashed potato, shredded cabbage and diced onion together in a bowl. Season well with salt, pepper and a splash of Worcestershire sauce if using.
Shape the mixture into 4 flat patties with your hands. Chill in the fridge for 10 minutes if you have time - they hold together better.
Heat the oil in a large frying pan over medium-high heat. Add the patties and fry for 4-5 minutes on each side until golden and crispy. Do not move them too early or they will break apart.
While the bubble and squeak is frying, heat the butter in another pan and fry the eggs to your liking - runny yolks are best.
Place a bubble and squeak patty on each plate and top with a fried egg. Season with extra pepper and serve with brown sauce or ketchup.