Start boiling the potatoes because they take ages to cook.
Cook the carrots until just done.
Simmer the fish in another saucepan with 4 fl.oz. of milk for about 10 minutes until cooked through.
Remove the fish with a slotted spoon and reserve the milk.
When the potatoes are cooked, mash them up with some of the uncooked milk and a good slab of butter.
Preheat the oven to 400° F (200°C).
Melt another chunk of butter in a saucepan. Add the flour and whisk together. Remove from heat. Pour in the reserved milk and the leftover milk. Stir constantly.
Return the pan to the heat, bring to a boil, keep stirring.
Reduce the heat and simmer until thickened, stirring all the time.
Combine the sauce with the fish, the parsley, the carrots and the black pepper.
Pour into an ovenproof dish.
Spread the mashed potatoes on top. Sprinkle with the grated cheese.
Bake for 20-30 minutes until golden.