Put a layer of potato slices in the base of a deepish, well-buttered baking dish and sprinkle with half the finely chopped onion.
Then mix the parsley, garlic, lemon zest and finely chopped anchovy fillets together and sprinkle a little of this mixture in the dish before adding another layer of potatoes, some onion and another sprinkling of parsley mixture.
Finish off with a final layer of potatoes (reserving a little of the parsley mixture).
Now bring the milk up to the boil, season, and then pour this over the potatoes, fleck the top with half the butter and bake (uncovered) for 40 minutes.
Meanwhile cut the fish into smallish cubes; then after the 40 minutes is up, put the fish on the top of the potatoes and sprinkle with the remaining parsley mixture and the remaining butter, and bake for a further 15-20 minutes, or until the fish is cooked.
Preheat the oven to 180˚C/350˚F/gas mark 4.