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Heat equal parts milk and water in a large pot (there should be enough liquid to cover all the ingredients). Add the salt cod, potatoes, herb bundle, carrot, celery, garlic head and onion. Bring slowly to a boil, and then turn off the heat as soon as it begins to boil. Let sit until the fish and potatoes are soft, 20 minutes. The fish should flake apart and the potatoes should not be crunchy. (If the potatoes need more time, remove the fish from the pot and cook the potatoes a little more.)
Transfer the cod and potatoes into a food processor with the pounded garlic cloves. Pour the cream into 1 container, and the olive oil into another. Turn the food processor on and gradually pour in the cream and oil in thin streams. The brandade will start to emulsify and get fluffy. (The brandade should be spreadable and even. You may not use all of the oil and cream, you may have to add a little more.) Turn off the processor and add salt and lemon juice to taste.
This recipe was provided by a chef, restaurant or culinary professional and makes a large quantity. The Food Network Kitchens have not tested it for home use and therefore cannot make any representation as to the results.