In a large bowl, soak the cod in enough cold water to cover for at least 24 hours and up to 2 days, changing the soaking water several times.Advertisement
In a small saucepan, combine soaked cod, garlic, bay leaf, milk, and the water. Bring to a simmer over medium heat; continue cooking until fish flakes when pierced with a fork, 15 to 20 minutes. Discard garlic and bay leaf. Using tongs or a slotted spoon, transfer cod to the bowl of a food processor fitted with the metal blade. Process until smooth.
Place potatoes in a small saucepan, and cover with cold water by 1 inch. Bring water to a boil, and add salt. Reduce heat to a simmer; cook over medium heat until potatoes are fork-tender, 15 to 20 minutes. Transfer to a colander to drain.
While still warm, pass potatoes through a ricer or a food mill fitted with the medium disk into a large bowl. Add pureed cod, olive oil, and cream; stir until completely combined and smooth. Keep covered until ready to use.