Preheat the oven to 450 degrees F (230 degrees C). Lightly grease a baking dish and place it on a baking sheet.

Rinse salt cod under cold water, transfer to a sealable container and cover with several inches of cold water. Soak cod in the refrigerator, changing the water every few hours, for 24 to 36 hours. Remove cod from water and cut into evenly sized pieces.

Stir cod, milk, thyme, bay leaves, and cayenne pepper together in a pot over medium-high heat. Cook until fish begins to flake; 7 to 15 minutes. Remove from heat and strain; reserve cooking liquid and transfer fish to a bowl.

Place potatoes and garlic in a large pot and cover with water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain.

Mash cod, a few splashes of reserved cooking liquid, and lemon zest together in a large bowl. Pour in remaining reserved cooking liquid and potatoes; mash until desired consistency is reached. Stir in 1/2 of the olive oil, lemon juice, and black pepper until smooth. Add remaining olive oil and blend until smooth. Season with salt. Pour mixture into the prepared baking dish. Spread crème fraîche over the top and score with a spoon to create a crisscross pattern.

Bake in the preheated oven until browned and bubbling, about 20 minutes