Start by boiling the potatoes in a pot of salted water for about 15 minutes, or until they are fork-tender. Drain and mash them in a mixing bowl.
In another pot, steam the white fish for about 10 minutes until it flakes easily with a fork. Remove the skin and bones, then add to the bowl with the mashed potatoes.
Stir in the grated carrot, parsley, lemon juice, and beaten egg until everything is well combined.
Using your hands, shape the mixture into small cakes, about 4 cm in diameter.
Coat each cake lightly with breadcrumbs.
Heat the olive oil in a frying pan over medium heat. Fry the fish cakes in batches for about 3-4 minutes on each side, until golden brown and cooked through.
Transfer the fish cakes to a baking tray and let them rest for 5 minutes before serving.
