1. The day before, desalt the salt cod fillets by soaking them in a large volume of cold water. Rinse them, change the water, and soak them again, repeating this process 2-3 times. Let them soak overnight in cold water.
2. On the same day.
Crush the garlic.
Chop the parsley.
Chop the onion.
Peel and cut the potatoes into pieces.
Remove any bones and skin from the salt cod, if any.
Preheat the oven to 200°C (392°F).
3. Cook the potatoes in boiling water. Drain them when they are fully cooked and mash them with a potato masher. Add the butter and the milk that you have heated. Whisk your mashed potatoes vigorously while gradually adding almost all of the olive oil (keep a little bit to sauté your onions). Keep your mashed potatoes warm.
4. Sauté the onions, crushed garlic, and chopped parsley in olive oil without browning.
5. As soon as your onions start to become translucent and slightly golden, add the salt cod fillets. Cook over low heat for a few minutes, crumbling the salt cod fillets with a spatula.
6. Incorporate your crumbled salt cod fillets into the mashed potatoes and mix everything well.
Put your salt cod brandade with mashed potatoes in a gratin dish and smooth the brandade with a fork. Bake the salt cod brandade with mashed potatoes for 15 minutes, then remove it from the oven.
7. Serve accompanied with a green salad.