For the Barnsley chop, heat a frying pan until hot, add the black pudding and cook until crisp and golden-brown. Remove the black pudding from the pan and set aside to drain on kitchen paper.
Place 200g/7oz of the butter into a bowl with the grated apple, then crumble in the cooled black pudding.
Mix well then place onto a sheet of greaseproof paper, shape into a log and roll up tightly. Chill in the fridge for at least one hour.
Preheat the oven to 200C/400F/Gas 6.
Heat an ovenproof frying pan until hot, add 25g/1oz of the remaining butter and the olive oil and heat until just foaming. Season the Barnsley chop with salt and freshly ground black pepper, and fry on each side for 1-2 minutes, or until golden-brown. Transfer to the oven and cook for another 5-6 minutes, or until just cooked.
Cut the chilled black pudding butter into 1cm/½in thick discs.
Remove the Barnsley chop from the oven, place the butter discs on top and set aside to rest for five minutes.
Meanwhile, heat a lidded saucepan until hot, add the remaining 25g/1oz butter, the apple and the water and cook for a couple of minutes. Cover with the lid and cook for 3-4 minutes, or until soft and fluffy, then beat with a wooden spoon to a smooth purée. Season with a touch of salt and freshly ground black pepper.
For the sautéed potatoes, black pudding and apples; heat half of the butter and the olive oil a large frying pan until foaming. Add the diced potatoes and cook for 1-2 minutes, then add the crumbled black pudding and cook for another 2-3 minutes until the potatoes are tender and the black pudding crisp.
Meanwhile, heat another frying pan until hot, add the remaining butter and the apples and cook for 2-3 minutes until caramelised. Stir the apples into the potato mixture and stir until well combined. Season with salt and freshly ground black pepper.
To serve, spoon the potato mixture in a line along one side of each serving plate with a spoonful of apple purée next to it. Place the Barnsley chop on top of the purée and spoon any melted black pudding butter over the top.