Heat the butter in a small frying pan over a medium heat. Once foaming, add the apple. Fry for 2 mins until beginning to caramelise, then remove with a slotted spoon onto a plate. Add the black pudding to the butter and cook for a further 2 mins, turning halfway until crispy. Remove with a slotted spoon and set aside with the apple.
Whisk the mustard, honey and vinegar into the butter and cook for 30 secs. Taste for seasoning and set aside on a very low heat to keep warm
Heat the oil in a large, heavy-bottomed saucepan until it reads 190C on a thermometer, or a piece of bread browns in it within 15 secs. Carefully drop in the sprouts and cook for 3 mins until deep golden brown. Drain on kitchen paper, then scatter with flaky sea salt. Divide the sprouts between two plates, along with the watercress, apple and black pudding, then drizzle over the warm dressing.