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Preheat the oven to 170C/Gas 3.
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Heat a large ovenproof frying pan until hot and add the olive oil.
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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.
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Preheat the vegetable oil in a deep fat fryer to 160C. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
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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.
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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.
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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.
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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.
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Add the parsley and cider vinegar and season, to taste, with salt and freshly ground black pepper.
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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.