Preheat the oven to 170C/340F/Gas 3.
Heat a large ovenproof frying pan until hot and add the olive oil.
Season the pork cutlets on both sides with salt and freshly ground black pepper and place in the frying pan. Cook, turning once, until golden-brown on both sides, then transfer to the oven to roast for 6-8 minutes, or until completely cooked through.
Preheat the vegetable oil in a deep fat fryer to 160C/325F. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Mould the black pudding meat into golf ball-sized balls, then dredge in plain flour. Dip the floured black pudding into the beaten egg, then dip into in the breadcrumbs to completely coat.
Deep-fry the black pudding balls for 3-4 minutes, or until golden-brown and completely cooked through. Carefully remove with a slotted spoon and drain onto kitchen paper.
For the ragout, melt one tablespoon of the butter in a pan over a low heat. Add the apple cubes and gently cook for 2-3 minutes avoiding any colouring of the fruit.
Add the white beans and the chicken stock and bring to the boil. Cook to reduce the liquid volume by half, then add the remaining two tablespoons of butter.
Add the parsley and cider vinegar and season, to taste, with salt and freshly ground black pepper.
To serve, divide the ragout among four serving bowls. Place a pork cutlet on top of each and place a black pudding ball alongside each.