Peel, wash and halve the potatoes, cover and cook in salted water for about 20 minutes. Peel, wash and slice carrots. Heat 1 tablespoon butter in a pot. Sauté the carrots for about 5 minutes while turning.
Add cream, bring to the boil and simmer for about 8 minutes. Season to taste with salt and 1 pinch of sugar.
Crumble cornflakes on a large flat plate. Wash the cod, dab dry and cut 4 pieces. Season with salt and some pepper. Whisk the egg in a deep plate. Turn the fish one after the other first in flour, then in egg and finally in cornflakes, press lightly.
Heat 2 tablespoons of oil in a frying pan. Fry the fillets on each side for about 3 minutes at medium heat. Drain the potatoes. Add lukewarm milk and 2 tablespoons of butter to the potatoes. Mash everything finely.
Season to taste with salt and nutmeg. Arrange fish with carrots and mashed potatoes.