Soak in cold water to cover:
Refrigerate for 24 hours. Drain, rinse well, and remove any skin and bones. Set aside. Place in a medium saucepan:
Add cool water to cover and bring to a boil. Reduce the heat to a simmer and cook until the potato is tender, about 15 minutes. Transfer the potato to a food processor with a slotted spoon. Bring the water back to a boil, add the fish, and remove from the heat. Let stand for 15 minutes, then drain and pat dry. Add the fish to the food processor, along with:
Pulse until the fish is finely chopped. With the machine running, add in a slow stream:
Process until the mixture is the consistency of mashed potatoes. Season to taste with:
The brandade may be made up to 2 days in advance. To serve, preheat the oven to 400°F. Spread the brandade into a shallow baking dish and bake until browned, about 15 minutes. Serve warm with: