Heat half the oil in a large frying pan, add the onions and cook over a gentle heat for about 10 minutes or until softened. Remove from the pan and set aside.
Add the remaining oil to the pan, tip in the potatoes and fry over a fairly high heat until starting to brown, turning them over regularly with a large spoon or spatula. Stir in the chopped sprouts and season with salt and black pepper.
Cook for 5 minutes, stirring occasionally, then add the ham and mustard and return the onions to the pan. Fry for a further 5 minutes until everything is piping hot. Serve at once.