Preheat oven to 180°C/350°F/Gas Mark 4. Cut potatoes into 1 cm(½ in) slices and place in a large saucepan. Cover with cold water, add a few teaspoons of salt and bring to the boil, then cook 6 minutes. Drain in a colander — they should be about half cooked and not mushy.
Grease a 3 litre baking dish with half the butter and sprinkle with half the parmesan. Bring cream and remaining butter to the boil in a pot. Add anchovies, parsley and salt and pepper to taste. Place half the potato slices in the bottom of the dish and pour on half the cream mixture. Lay remaining potatoes on and pour over the rest of the cream, then sprinkle with remaining cheese. Cover the dish with a lid or foil and bake 35 minutes. Remove lid and cook until potatoes are tender and the crust is golden.