Step 1Soak the salt cod in cold water overnight, changing water several times.
Step 2The next day, combine the cream, bay leaves, allspice, juniper berries, coriander and hot peppers in a small saucepan. Add the 6 whole garlic cloves and bring to a simmer. Cook over very low heat 30 minutes, until thickened and well flavored.
Step 3While the cream steeps, bring a second pot of water to a boil with ginger. Add the cod and return to a boil. Immediately remove with a slotted spoon to a colander to drain. Let stand until cool enough to handle.
Step 4Boil the potato until soft; drain.
Step 5Flake the cod with fingers or forks until very fine and place in mixing bowl; discard skin if necessary. Add the potato and mash together. Strain the cream through a fine sieve into the mixture, discarding solids. Mix to a smooth puree. Add the remaining chopped garlic and mix well. Taste and add salt if needed.
Step 6Heat the oven to 425 degrees. Place the shiitakes in a large shallow bowl and sprinkle with olive oil. Toss until completely coated. Arrange on a large baking sheet in a single layer, stem side up. Mound about 1 tablespoon brandade into the center of each. Dust with paprika.
Step 7Roast 10 minutes. Cool slightly before serving.