For the rösti, place the grated potatoes into a clean tea towel inside a bowl and squeeze out any excess water into the bowl.
Transfer the grated potato into a clean bowl along with the crème fraîche and egg yolk, stir to mix and season well with salt and freshly ground black pepper.
Heat the butter in an ovenproof frying pan over a medium heat and place 2 x 7.5cm/3in chefs' rings into the pan.
Spoon the potato mixture into the rings, press down well with a spoon and cook for 3-4 minutes, or until golden brown. Turn the ring over, press the mixture down and cook for 3-4 minutes on the other side.
Transfer the pan to the oven and bake the rösti for 5-10 minutes, or until tender and cooked through.
Meanwhile, for the black pudding, heat the oil in a small frying pan until hot, place the black pudding into the pan and cook until golden-brown and cooked through.
For the apples, heat the butter in another pan, add the apple segments, stirring to coat in the butter, and cook until golden-brown. Add the cider to the pan and simmer until no liquid remains.
To serve, place the rösti onto a serving plate and top with the black pudding and apples.