Heat half the fat in a non-stick frying pan. Add the onion and fry over a medium heat until translucent. Add the sprouts and cook until everything is starting to caramelise around the edges. Transfer to a bowl.
Roughly mash the leftover root vegetables together, then add them to the onion and sprouts. Season well.
Heat the remaining fat in the frying pan. Pile the mixture back in, pressing down. Cook until the base has a really good crust on it. Carefully go round the edges with a palette knife to make sure it will come away easily (it won’t if the crust hasn’t cooked for long enough), then flip onto a plate, before sliding it back, cooked side up, into the pan.
Cook until another crust forms, then serve. (Alternatively, you can wait for a crust to form, break it all up and flatten down again, repeating a couple of times until the bubble and squeak is a mixture of mash and well browned, crisp nuggets of crust.)