Note that the salt cod needs to be soaked for 24 hours, with a change of water every six to eight hours and a thorough rinsing at the end. You can continue to store the soaked cod for two to three more days in the refrigerator, so long as you keep it immersed in water and continue to change the water daily.
Melt the butter in a large sauté pan over medium heat and add the breadcrumbs. Toast, stirring often, until the breadcrumbs are golden brown and evenly toasted, 10-12 minutes. Stir in the parsley and thyme and season gently with salt. Let cool to room temperature. If necessary, store in an airtight container at room temperature for up to 2 weeks.
Soak the cod in a covered container in the refrigerator for 24 hours, changing the water at least once. Drain the fish, rinse thoroughly, drain again, and cut into large chunks.
Place a rack in the middle position in the oven and preheat to 375 degrees.
In a saucepan, cover the salt cod in water and boil until the chunks of fish are easy to flake into smaller pieces with a fork but remain somewhat firm, about 20 minutes. Drain.
Meanwhile, in a separate small saucepan, combine the potato, cream, bay leaf, and rosemary. Simmer over low heat until the potatoes are tender and the mixture has reduced in volume by about 1/3, 10-12 minutes. Remove the bay leaf and the rosemary stem (the leaves will have fallen off).
Drain the potatoes over a bowl to catch the cream. While the potatoes are still warm, combine them in a food processor with the cod, onions, and garlic and purée the mixture, slowly adding the reserved cream, until it is very smooth. Transfer the brandade to a shallow casserole and top with breadcrumbs. Bake the brandade until it is hot all the way through and the top is golden brown, 15-18 minutes. Serve with sliced baguette.