Cook the potatoes and the apple in boiling salted water for 20 minutes. Drain well and mash with the butter, salt and freshly ground black pepper.
Preheat the oven to 200C/400F/Gas 6.
Mash the black pudding with a fork and gently fry in a hot pan for two minutes, turning, until crisp.
Place an oiled ring mould measuring 8cm/3¼in wide by 6cm/2½in high on a baking tray lined with greaseproof paper, and arrange a layer of black pudding at the base, pressing down gently.
Top with a layer of mash, then repeat, finishing with a layer of potato.
Gently remove the mould and repeat until you have four cakes.
Scatter with cheese and bake for 15 minutes to heat through. Finish under a hot grill if not golden brown.
For the sauce, gently heat the cream, mustard, salt and freshly ground black pepper, stirring frequently.
Transfer the cakes to warm plates, top with the salad greens, and serve with the mustard sauce.