1. Prepare the cod. Soak it in fresh water for 24 hours, changing the water and rinsing the fish 4 to 6 times. On the same day, drain the cod, rinse it, and place it in a saucepan. Cover with cold water, bring to a simmer, and cook for 8 to 10 minutes. Drain and let it cool. Remove the skin and bones. Flake the cod with your fingers.
2. In a sauté pan, heat 4 tablespoons of oil. In a saucepan, heat the milk. In another small saucepan, gently heat the remaining oil.
3. Place the pieces of cod in the sauté pan, stir gently. Pour the hot milk alternating with a little hot oil. Mix gently, wait for the cod to absorb everything before pouring more milk and oil. Add 2 peeled, germ-free, and chopped garlic cloves, the mashed potato, the remaining milk and oil. The consistency should be creamy, while still retaining pieces of cod. Season generously with pepper and salt if necessary.
4. Preheat the oven to 220°C (425°F). Prepare the sage breadcrumb topping. In a food processor, chop the sage with the softened butter, breadcrumbs, crushed hazelnuts, 1 peeled and germ-free garlic clove, salt, and pepper.
5. Rub a gratin dish with the last peeled garlic clove. Fill it with the salt cod brandade, sprinkle the top with the sage breadcrumb mixture. Bake until the brandade is gratinated. Serve immediately, with a green salad for example.