Cut the potatoes into large, even chunks and cook in a large pan of boiling salted water for 10-15 minutes or until tender. Drain then mash and cool slightly.
Put the haddock in a frying pan, skin side up, cover with water and bring to the boil. Cover with a lid and gently simmer for 5 minutes until the fish flakes easily. Drain the fish, peel away the skin.
Flake the fish and add to the mash with 50g of the Parmigiano Reggiano, horseradish and parsley, then gently mix together. Season to taste. Divide into 4, then shape each into a neat round.
In a shallow bowl, mix the remaining Parmigiano Reggiano with the breadcrumbs. Pour the egg into another shallow bowl; and sprinkle the flour onto a plate. Coat the cakes in flour, then dip in egg and finally the breadcrumb mixture until well coated.
Repeat to make 4 large cakes.
Heat 2 cm vegetable oil in a deep-frying pan and cook the cakes over a medium low heat for 8 minutes, turning once until golden on each side. Drain on kitchen paper and repeat with the remainder keeping them warm in the oven.
Serve hot with a watercress salad