At first, this appetizer may seem tricky to make, but it’s actually no more difficult than mashed potatoes. Just make sure to plan ahead, so you have enough time to allow the cod to soak and release its salt. Since this is one of the quintessential dishes of the region – and addictive, especially when served with aioli – it’s definitely worth the effort.
In a large bowl, cover cod with cold water, wrap with Saran wrap, and refrigerate for 24 hours. (Over the course of 24 hours, change the water 4 to 5 times.) Drain the cod, place in a saucepan, and cover it with cold water by at least 2 inches. Bring to a simmer and remove from heat. Drain cod, flake it, and place into a large bowl.
In a medium bowl, add yolks, mustard, lemon juice, and a healthy pinch of salt. Slowly drizzle in 1 cup oil, whisking constantly, until mixture has emulsified. When all oil has been added, whisk an additional 15 seconds. Add garlic and mix well. Cover and set aside.
In a medium saucepan, cover potatoes with cold water and bring to a boil. Cook until potatoes are tender, about 20 minutes, and drain. Pass potatoes through a ricer and add to cod.
In a separate medium saucepan, bring cream, garlic, and thyme to a simmer and cook for 5 minutes. Allow mixture to cool slightly and pour into food processor or blender. Purée for 1 minute. Add cream and parsley to cod mixture. Using an electric mixture, whip cod, cream, and potato until combined. Gradually add oil and whip until just incorporated. Add lemon juice and season with salt and pepper.
Serve with aioli and toasted brioche, baguette, or crackers.