Desalt the cod by soaking it in cold water for 36 to 48 hours before preparing the brandade (changing the water regularly).
Peel and cut the potatoes into pieces. Cook them for about 20 minutes in a pot of boiling water. Once your potatoes are cooked, mash them with a fork. Add a large knob of butter and the hot milk. Mix vigorously while adding the olive oil little by little. Keep warm.
Fry the finely chopped onion and garlic and pour them over the potatoes.
Crumble cod with your fingers or a fork and mix with the crushed potatoes and chopped parsley.
Season with pepper and place in a baking dish.
Bake for 15 to 20 minutes in a preheated oven at 180°C. Grill under the broiler, keeping an eye on the cooking time before serving with a few sprigs of chopped chives on top.